Generation of multivariate Hermite interpolating polynomials:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2006
|
| Schriftenreihe: | Pure and Applied Mathematics
274 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 672 Seiten graph. Darst. |
| ISBN: | 1584885726 9781584885726 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV026753690 | ||
| 003 | DE-604 | ||
| 005 | 20210601 | ||
| 007 | t | ||
| 008 | 110326s2006 d||| |||| 00||| eng d | ||
| 015 | |a GBA572182 |2 dnb | ||
| 020 | |a 1584885726 |9 1-584-88572-6 | ||
| 020 | |a 9781584885726 |9 978-1-584-88572-6 | ||
| 035 | |a (OCoLC)634650001 | ||
| 035 | |a (DE-599)HBZHT014517339 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-188 |a DE-83 | ||
| 082 | 0 | |a 515.55 | |
| 084 | |a SK 680 |0 (DE-625)143252: |2 rvk | ||
| 084 | |a 41A05 |2 msc | ||
| 084 | |a 41A63 |2 msc | ||
| 100 | 1 | |a Tavares, Santiago Alves |e Verfasser |0 (DE-588)137922124 |4 aut | |
| 245 | 1 | 0 | |a Generation of multivariate Hermite interpolating polynomials |c Santiago Alves Tavares, University of Florida, Gainesville, FL, U.S.A. |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b Chapman & Hall/CRC |c 2006 | |
| 300 | |a 672 Seiten |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and Applied Mathematics |v 274 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 4 | |a Hermite polynomials | |
| 650 | 4 | |a Multivariate analysis | |
| 830 | 0 | |a Pure and Applied Mathematics |v 274 |w (DE-604)BV000001885 |9 274 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022290876&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-022290876 | ||
Datensatz im Suchindex
| _version_ | 1804145370891026432 |
|---|---|
| adam_text | GENERATION OF MULTIVARIATE HERMITE INTERPOLATING POLYNOMIALS SANTIAGO
ALVES TAVARES UNIVERSITY OF FLORIDA GAINESVILLE, FL, U.S.A. CHAPMAN &.
HALL/CRC TAYLOR & FRANCIS GROUP BOCA RATON LONDON NEW YORK SINGAPORE
CONTENTS I CONSTRAINED NUMBERS 1 1 CONSTRAINED COORDINATE SYSTEM 3 1.1
DEFINITION . : 3 1.1.1 OPERATIONS WITH CONSTRAINED NUMBERS 12 1.1.2
OPERATIONS WITH SETS OF CONSTRAINED NUMBERS 14 1.2 GEOMETRIC
REPRESENTATION 19 1.2.1 CONTRAVARIANT COORDINATE REPRESENTATION 19 1.2.2
COVARIANT COORDINATE REPRESENTATION (DUAL SYSTEM) . . 20 1.3
VISUALIZATION OF THE COORDINATE AXES 22 1.3.1 ORTHOGONAL REPRESENTATION
OF THE COORDINATE AXES ... 22 1.3.2 OBLIQUE REPRESENTATION OF THE
COORDINATE AXES 22 1.4 GEOMETRIC LOCATION OF THE CONSTRAINED NUMBERS 23
1.4.1 ONE-DIMENSIONAL CONSTRAINED NUMBERS 23 1.4.2 TWO-DIMENSIONAL
CONSTRAINED NUMBERS 24 1.5 TWO-DIMENSIONAL REPRESENTATION OF
N-DIMENSIONAL COORDINATE AXES 25 1.6 ZERO-DIMENSIONAL CONSTRAINED SPACE
26 1.6.1 DEFINITIONS 26 1.6.2 GEOMETRIC REPRESENTATION OF THE
ZERO-DIMENSIONAL CON- STRAINED NUMBERS 27 2 GENERATION OF THE COORDINATE
SYSTEM 31 2.1 GENERATION AS A CARTESIAN PRODUCT OF TWO SETS 31 2.1.1
ONE-DIMENSIONAL CONSTRAINED NUMBERS 31 2.1.2 TWO-DIMENSIONAL CONSTRAINED
NUMBERS 32 2.1.3 5-DIMENSIONAL CONSTRAINED NUMBERS 33 2.2 GENERATION OF
THE ELEMENTS OF THE SET LJ FOR THE UNDERLYING SET Z , . 33 2.2.1 RULES
FOR THE GENERATION 33 2.2.2 RULES FOR THE PARTICULAR CASES 36 2.2.3
ALGORITHM FOR THE GENERATION OF THE ELEMENTS 37 2.3 GENERATION OF THE
ELEMENTS OF THE SET L S () FOR THE UNDERLYING SETZ 38 2.3.1 ALGORITHM
FOR THE GENERATION OF THE ELEMENTS 38 2.4 GENERATION OF THE ELEMENTS OF
THE SET L FOR THE UNDERLYING SET Z 40 2.4.1 RULES FOR THE GENERATION 40
2.4.2 RULES FOR THE PARTICULAR CASES 43 2.4.3 ALGORITHM FOR THE
GENERATION OF THE ELEMENTS OF THE SET L USING THE COORDINATE NUMBERS 43
2.4.4 ALGORITHM FOR THE GENERATION OF THE ELEMENTS OF THE SET L USING
SUBLEVELS 45 2.5 GENERATION OF THE ELEMENTS OF THE SET L S () FOR THE
UNDERLYING SET Z + 46 2.5.1 ALGORITHM FOR THE GENERATION OF THE ELEMENTS
OF THE SET L 5 () USING THE COORDINATE NUMBERS 47 2.5.2 ALGORITHM FOR
THE GENERATION OF THE ELEMENTS OF THE SET L S (T) USING SUBLEVELS 48 2.6
EXAMPLES OF ZERO-DIMENSIONAL CONSTRAINED SPACE 49 2.6.1 GENERATION OF
THE ELEMENTS 49 R 2.6.2 ELEMENTS OF THE SET LG AND L(0) 50 2.6.3
ELEMENTS OF THE SET L 50 2.6.4 ELEMENTS OF THE SET L() 51 2.6.5
GEOMETRIC REPRESENTATION OF THE SET L 52 2.6.6 GEOMETRIC REPRESENTATION
OF THE SET L() 52 2.7 EXAMPLES OF ONE-DIMENSIONAL CONSTRAINED SPACE 53
2.7.1 GENERATION OF THE ELEMENTS 53 2.7.2 ELEMENTS OF THE SET L AND L L
(0) 55 2.7.3 ELEMENTS OF THE SETS L AND L^L) 56 2.7.4 ELEMENTS OF THE
SET L AND L 1 (2) 60 2.7.5 ELEMENTS OF THE SET L AND L 1 (3) 65 2.8
EXAMPLES OF TWO-DIMENSIONAL CONSTRAINED SPACE 70 2.8.1 GENERATION OF THE
ELEMENTS 70 2.8.2 ELEMENTS OF THE SET L AND L 2 (0) 72 2.8.3 ELEMENTS
OF THE SETS L AND L 2 (L) 73 2.8.4 ELEMENTS OF THE SET L AND L 2 (2)
77 2.8.5 ELEMENTS OF THE SET L AND 1? (3) 85 2.9 EXAMPLES OF
THREE-DIMENSIONAL CONSTRAINED SPACE 91 2.9.1 GENERATION OF THE ELEMENTS
92 2.9.2 ELEMENTS OF THE SET L% AND L 3 (0) 95 2.9.3 ELEMENTS OF THE
SETS LF AND L 3 (L) 95 2.9.4 ELEMENTS OF THE SET L AND L 3 (2) 98 2.9.5
ELEMENTS OF THE SET L AND L 3 (3) 101 2.10 PROPERTIES OF SETS OF
CONSTRAINED NUMBERS 106 NATURAL COORDINATES 113 3.1 ONE-DIMENSIONAL
NATURAL COORDINATE NUMBERS 113 3.1.1 LOCATION OF A POINT 113 3.1.2
RELATION BETWEEN THE ONE-DIMENSIONAL NATURAL COORDI- NATE NUMBERS AND
THE ONE-DIMENSIONAL CARTESIAN COOR- DINATE NUMBERS 114 3.1.3 RELATION
BETWEEN THE ONE-DIMENSIONAL NATURAL COORDI- NATE NUMBERS AND THE
TWO-DIMENSIONAL CARTESIAN COOR- DINATE NUMBERS 116 3.2 TWO-DIMENSIONAL
NATURAL COORDINATE NUMBERS 117 3.2.1 LOCATION OF A POINT 117 3.2.2
RELATION BETWEEN THE TWO-DIMENSIONAL NATURAL COORDI- NATE NUMBERS AND
THE TWO-DIMENSIONAL CARTESIAN COOR- DINATE NUMBERS 120 3.2.3 COORDINATES
ORTHOGONAL TO THE SIDES OF THE TRIANGLE . . 121 3.3 THREE-DIMENSIONAL
NATURAL COORDINATE NUMBERS 123 3.3.1 LOCATION OF A POINT 123 3.3.2
RELATION BETWEEN THE THREE-DIMENSIONAL NATURAL COORDI- NATE NUMBERS AND
THE THREE-DIMENSIONAL CARTESIAN COOR- DINATE NUMBERS 125 3.3.3
COORDINATES ORTHOGONAL TO THE FACES OF THE TETRAHEDRON 126 3.4
(5-DIMENSIONAL NATURAL COORDINATE NUMBERS * 128 3.4.1 LOCATION OF A
POINT . . . 128 3.4.2 RELATION BETWEEN THE ^-DIMENSIONAL NATURAL
COORDINATE NUMBERS AND THE 5- DIMENSIONAL CARTESIAN COORDINATE NUM- BERS
128 3.4.3 COORDINATES ORTHOGONAL TO THE FACES OF THE 6-HEDRON . 130 4
COMPUTATION OF THE NUMBER OF ELEMENTS 135 4.1 ZERO-DIMENSIONAL
CONSTRAINED SPACE 135 4.1.1 UNDERLYING SET Z 135 4.1.2 UNDERLYING SET Z
+ 137 4.1.3 SUMMARY FOR THE ZERO-DIMENSIONAL SPACE 138 4.2
ONE-DIMENSIONAL CONSTRAINED SPACE 139 4.2.1 UNDERLYING SET Z 139 4.2.2
UNDERLYING SET Z + 142 4.2.3 SUMMARY FOR THE ONE-DIMENSIONAL NUMBERS 149
4.3 TWO-DIMENSIONAL SPACE 150 4.3.1 UNDERLYING SET Z 150 4.3.2
UNDERLYING SET Z + 155 4.3.3 SUMMARY FOR THE TWO-DIMENSIONAL NUMBERS 162
4.4 THREE-DIMENSIONAL CONSTRAINED SPACE 163 4.4.1 UNDERLYING SET Z 163
4.4.2 UNDERLYING SET Z + 166 4.4.3 SUMMARY FOR THE THREE-DIMENSIONAL
NUMBERS 169 4.5 (5-DIMENSIONAL CONSTRAINED SPACE 170 4.5.1 UNDERLYING
SET Z + 170 4.6 SUMMARY . . .- 171 4.6.1 IF THE UNDERLYING SET IS Z 171
4.6.2 IF THE UNDERLYING SET IS Z + 173 4.7 MATHEMATICAL TOOLS 175 4.7.1
SUM OF THE TERMS OF AN ARITHMETIC PROGRESSION 175 4.7.2 SUM OF SQUARES
175 4.7.3 SUM OF CUBES 177 4.7.4 SELECTED COMBINATORICS PROPERTIES 178
4.7.5 POCHHAMMER S SYMBOL 184 5 AN ORDERING RELATION 185 5.1 DEFINITION
OF ORDER 185 5.1.1 POSSIBLE DEFINITIONS 185 5.1.2 ADOPTED DEFINITION 187
5.2 INTEGER NUMBERS AS THE UNDERLYING SET 191 5.2.1 ZERO-DIMENSIONAL
CONSTRAINED SPACE 191 5.2.2 ONE-DIMENSIONAL CONSTRAINED SPACE 191 5.2.3
TWO-DIMENSIONAL CONSTRAINED SPACE 195 5.2.4 THREE-DIMENSIONAL
CONSTRAINED SPACE 200 5.3 NONNEGATIVE INTEGER NUMBERS AS THE UNDERLYING
SET 204 5.3.1 ZERO-DIMENSIONAL CONSTRAINED SPACE 204 5.3.2
ONE-DIMENSIONAL CONSTRAINED SPACE 205 5.3.3 TWO-DIMENSIONAL SPACE 207
5.3.4 GENERALIZATION FOR THE CONSTRAINED NUMBERS 209 5.4 PROPERTIES OF
THE ORDERING FUNCTION 210 5.5 SUMMARY 211 5.5.1 SUMMARY FOR THE
UNDERLYING SET IS Z 211 5.5.2 SUMMARY FOR THE UNDERLYING SET IS Z 214 6
APPLICATION TO SYMBOLIC COMPUTATION OF DERIVATIVES 217 6.1 POLYNOMIAL
NOTATION 217 6.1.1 EXAMPLES 217 6.1.2 NOTATION FOR A COMPLETE POLYNOMIAL
219 6.1.3 EXAMPLES . . 220 6.1.4 NOTATION FOR THE TERMS IN THE LEVEL
OF COMPLETE POLY- NOMIALS 223 6.2 PARTIAL DERIVATIVE NOTATION 224 6.3
DERIVATIVE OF ORDER V OF A POLYNOMIAL 225 6.3.1 POLYNOMIALS WHOSE POWERS
ARE ELEMENTS IN THE SET Z 226 6.3.2 POLYNOMIAL WHOSE POWERS ARE ELEMENTS
IN THE SET Z . . 228 6.3.3 ALGORITHM TO OBTAIN THE DERIVATIVE OF A
POLYNOMIAL WHOSE POWERS ARE ELEMENTS IN THE SET Z 229 6.3.4 ALGORITHM TO
OBTAIN THE DERIVATIVE OF A POLYNOMIAL WHOSE POWERS ARE ELEMENTS IN THE
SET Z 229 6.4 PARTIAL INTEGRATION NOTATION 230 6.4.1 INTEGRATION OF
ORDER V OF A POLYNOMIAL 231 6.5 ELEMENTS CHARACTERIZING A POLYNOMIAL 233
6.6 ORDER OF DERIVATIVE 236 6.7 DERIVATIVE OF THE PRODUCT OF FUNCTIONS
IN ONE VARIABLE . . . . 236 6.7.1 DERIVATIVE OF THE PRODUCT OF TWO
FUNCTIONS USING CON- STRAINED MULTIPLICATION 236 6.7.2 DERIVATIVE OF THE
PRODUCT OF T FUNCTIONS USING CONSTRAINED MULTIPLICATION 238 6.7.3
DERIVATIVE OF THE PRODUCT OF TWO FUNCTIONS IN ONE VARI- ABLE 239 6.7.4
DERIVATIVE OF THE PRODUCT OF THREE FUNCTIONS IN ONE VARI- ABLE 241 6.7.5
DERIVATIVE OF THE PRODUCT OF T FUNCTIONS IN ONE VARIABLE 243 6.8
DERIVATIVE OF A PRODUCT OF FUNCTIONS OF SEVERAL VARIABLES . . . 246
6.8.1 DERIVATIVE OF A PRODUCT OF TWO FUNCTIONS OF TWO VARIABLES 246
6.8.2 DERIVATIVE OF THE PRODUCT OF T FUNCTIONS OF D VARIABLES 253 6.9
EXPANSION OF THE POWER OF A SUM OF FUNCTIONS 263 6.9.1 EXPANSION OF THE
POWER OF A SUM OF TWO FUNCTIONS . . . 263 6.9.2 EXPANSION OF THE POWER
OF A SUM OF T FUNCTIONS . . . . 264 6.10 COMPUTATION OF THE DERIVATIVES
OF THE FORM L/(X * /3) S . . . . 265 6.10.1 ONE FUNCTION AND ONE
VARIABLE 265 6.10.2 PRODUCT OF T FUNCTIONS OF THE SAME VARIABLE X 267
6.10.3 COMPUTATION OF THE DERIVATIVES OF THE PRODUCT OF D FUNC- TIONS,
WHICH ARE PRODUCT OF KJ FUNCTIONS OF THE SAME VARIABLE XJ 272 6.10.4
SUMMARY 280 6.11 COMPUTATION OF THE DERIVATIVES OF THE FORM 1/ (C O X O
+ CIXI + C 2 ) 282 6.11.1 DERIVATIVE OF ONE FUNCTION 282 6.11.2
DERIVATIVE OF PRODUCT OF T FUNCTIONS 283 II HERMITE INTERPOLATING
POLYNOMIALS 285 7 MULTIVARIATE HERMITE INTERPOLATING POLYNOMIAL 287 7.1
DEFINITION 287 7.2 POLYNOMIAL CONSTRUCTION 290 7.2.1 THE POLYNOMIAL P E
(X) 290 7.2.2 THE POLYNOMIAL Q E , N ( X ) 302 7.2.3 THE POLYNOMIAL F
E N (A, X) 303 7.3 COMPUTATION OF THE COEFFICIENTS OF F E N (A, X) 307
7.3.1 HYPERSURFACE REGION 307 7.3.2 CONSTRUCTION OF THE SYSTEM OF
EQUATIONS 308 7.3.3 COMPUTATION OF THE TERM [I/P E (X)] (V) 308 7.3.4
COMPUTATION OF [F E N (A, X) {V) 309 7.3.5 SOLUTION OF THE SYSTEM OF
EQUATIONS 311 7.4 PROPERTIES OF THE HERMITE INTERPOLATING POLYNOMIALS
315 7.4.1 COMPUTATION OF THE COEFFICIENTS OF FH,N(G, X) IN TERMS OF THE
COEFFICIENTS OF F E ,N(A, X) IF THE REFERENCE NODES E AND H DIFFER ONLY
FOR ONE COORDINATE NUMBER 315 7.4.2 COMPUTATION OF THE COEFFICIENTS OF
FH,N{G, X) IN TERMS OF THE COEFFICIENTS OF / E , RA (O-, X) IF THE
REFERENCE NODES E AND H DIFFER FOR SEVERAL COORDINATE NUMBER 320 7.4.3
RELATION BETWEEN THE POLYNOMIALS *E?N(X)| X=Q AND * { $(X) X=A IF
V&IX)^ = { $(X) X=A 321 7.4.4 RELATION BETWEEN [L/(N!P E (Z))] H AND
[L/(N!P E (A:)] (/I) IF [I IS A PERMUTATION OF V 323 7.4.5 EQUALITY OF
THE COEFFICIENTS OF THE TERMS OF THE POLY- NOMIAL F ET7L (A,X) THAT ARE
IN THE SAME LEVEL AND WHICH INDICES ARE PERMUTATIONS 324 7.4.6
COMPUTATION OF THE POLYNOMIALS RELATED TO ONE NODE IN TERMS OF THE
POLYNOMIALS RELATED TO A SYMMETRIC NODE 332 8 GENERATION OF THE HERMITE
INTERPOLATING POLYNOMIALS 335 8.1 POLYNOMIALS OF MINIMUM DEGREE 335 8.2
THE DEGREE OF F E N (A, X) IS KEPT CONSTANT 337 8.2.1 THE DEGREE OF F E
,N(A ,X) IS R 337 9 HERMITE INTERPOLATING POLYNOMIALS: THE CLASSICAL
AND PRESENT APPROACHES 339 9.1 CLASSICAL APPROACH, ONE VARIABLE 339 9.2
COMPUTATION OF A ONE-VARIABLE POLYNOMIAL 341 9.2.1 GENERATING EXPRESSION
341 9.2.2 GENERATION OF THE POLYNOMIALS RELATED TO THE REFERENCE NODE A
= -1 342 9.2.3 CONSTRUCTION OF THE POLYNOMIAL $ AI O(X) 342 9.2.4
CONSTRUCTION OF THE POLYNOMIAL & A ,I(X) 346 9.2.5 CONSTRUCTION OF THE
POLYNOMIAL & A ,I {X) 349 9.2.6 GENERATION OF THE POLYNOMIALS RELATED
TO THE REFERENCE NODE 6=1 351 9.2.7 POLYNOMIAL $ B ,O( X ) * 351 9.2.8
POLYNOMIAL $ B ,I(X) 352 9.2.9 POLYNOMIAL $ B , 2 (A;) 352 9.3
COMPARISON BETWEEN THE TWO TECHNIQUES 353 9.3.1 CLASSICAL APPROACH 353
9.3.2 THE PRESENT APPROACH 353 10 NORMALIZED SYMMETRIC SQUARE DOMAIN 355
10.1 COMPUTATION OF A TWO-VARIABLE POLYNOMIAL 355 10.2 GENERATION OF THE
POLYNOMIAL $00,00(^0^1) RELATED TO THE REF- ERENCE NODE AO = (*1,-1) 355
10.2.1 ELEMENTS COMMON TO ALL POLYNOMIALS RELATED TO THE NODE A 0 =
(-1,-1) 356 10.2.2 GENERATION OF THE POLYNOMIAL $ AO ,00 (X O ,XI) 358
10.2.3 COMPUTATION OF THE COEFFICIENTS OF THE POLYNOMIAL /A O ,OO(A0 359
10.3 GENERATION OF THE POLYNOMIAL $00,10(^0; X I) RELATED TO THE REF-
ERENCE NODE DO = (*1,-1) 376 10.3.1 EXPRESSION FOR THE POLYNOMIAL $ A0)
10(2:0, A^I) 376 10.3.2 COMPUTATION OF THE POLYNOMIAL F AO ,N{X) 376
10.3.3 POLYNOMIAL * AO IO(X 0 ,XI) 385 10.3.4 SUMMARY OF THE
POLYNOMIALS & AO ,N RELATED TO THE REFER- ENCE NODE AO = (*1,-1) 386
10.4 GENERATION OF THE POLYNOMIALS $ AI ,N RELATED TO THE REFERENCE NODE
(1,-1) 388 10.4.1 GENERATION OF THE POLYNOMIALS $AI ,N 388 10.4.2
SUMMARY OF THE POLYNOMIALS $ AI ,N RELATED TO THE REFER- ENCE NODE A *
(1,-1) 389 10.5 GENERATION OF THE POLYNOMIALS & A2 ,N RELATED TO THE
REFERENCE NODE (1,1) 391 10.5.1 GENERATION OF THE POLYNOMIALS 391
10.5.2 SUMMARY OF THE POLYNOMIALS & A2 ,TI RELATED TO THE REFER- ENCE
NODE 2 = (1,1) 393 10.6 GENERATION OF THE POLYNOMIALS 3 A3 ,RA RELATED
TO THE REFERENCE NODE A 3 = (-1,1) 395 10.6.1 GENERATION OF THE
POLYNOMIALS 395 10.6.2 SUMMARY OF THE POLYNOMIALS $03 ;TL RELATED TO THE
REF- ERENCE NODE 03 = (*1,1) 396 10.7 GENERATION OF THE POLYNOMIAL $ AO
,OO(XO,XI) RELATED TO THE REF- ERENCE NODE, AO = (*1, *1) WITH Q = 6 398
10.7.1 COMPUTATION OF THE COEFFICIENTS OF THE POLYNOMIAL /A 0 ,OO(X) 398
10.7.2 SUMMARY OF THE POLYNOMIALS $ Q0 , N RELATED TO THE REFER- ENCE
NODE AO = (*1, *1) AND Q = 6 427 11 RECTANGULAR NONSYMMETRIC DOMAIN 433
11.1 GENERATION OF A TWO-VARIABLE POLYNOMIAL IN A RECTANGULAR NON-
SYMMETRIC DOMAIN 433 11.2 GENERATION OF THE POLYNOMIAL $ A3 ,OO(XO,XI)
RELATED TO THE REF- ERENCE NODE D3 = (2,4) 433 11.2.1 INFORMATION ABOUT
THE POLYNOMIAL 433 11.2.2 COMMON FACTORS RELATED TO THE REFERENCE NODE D
3 = (2,4) 435 11.2.3 EXPRESSION FOR THE POLYNOMIAL Q A3 ,N{X) 436 11.2.4
EXPRESSION FOR THE POLYNOMIAL & A3TN (X) 436 11.2.5 PROPERTIES OF THE
POLYNOMIAL $ A3I OO(^O,XI) 436 11.2.6 CONSTRUCTION OF THE CONSTANT TERM
N P A3 (A) 437 11.2.7 CONSTRUCTION OF THE POLYNOMIAL Q A3 ,N{X) ********
437 11.2.8 THE POLYNOMIAL $ A3JO O(XO,XI) 437 11.2.9 COMPUTATION OF THE
COEFFICIENTS OF THE POLYNOMIAL /O3,OO(A:) 437 11.3 SUMMARY OF THE
POLYNOMIALS 458 11.3.1 POLYNOMIALS E ,I RELATED TO THE NODE A * (6,12)
... 458 11.3.2 POLYNOMIALS $ E ,I RELATED TO THE NODE A 2 * (2,12) ...
460 11.3.3 POLYNOMIALS $ E ,N RELATED TO THE NODE D3 = (2,4) . . . 462
11.3.4 POLYNOMIALS $ E , RELATED TO THE NODE D 4 = (6,4) . . . . 464 12
GENERIC DOMAINS 467 12.1 EXPRESSION FOR THE POLYNOMIAL 467 12.1.1
INFORMATION ABOUT THE POLYNOMIAL 467 12.1.2 PROPERTIES OF THE POLYNOMIAL
$ A3I OO(XO,A;I) 468 12.2 EXPRESSION FOR THE POLYNOMIAL & E ,N{X) 469
12.2.1 COMMON FACTORS RELATED TO THE REFERENCE NODE O 3 = (-5,2) 472
12.2.2 EXPRESSION FOR THE POLYNOMIAL Q A3 ,N(X) 472 12.2.3 CONSTRUCTION
OF THE CONSTANT TERM N!P A3 (A) 472 12.2.4 CONSTRUCTION OF THE
POLYNOMIAL Q A3 , N (X) 472 12.2.5 THE POLYNOMIAL 3 A3 FIO( X O, X I)
473 12.2.6 COMPUTATION OF THE COEFFICIENTS OF THE POLYNOMIAL /A 3
,OO(A,X) 473 12.3 TRIANGULAR DOMAIN 474 12.3.1 INFORMATION ABOUT THE
POLYNOMIAL 474 12.3.2 COMMON FACTORS RELATED TO THE REFERENCE NODE D 0 =
(0, Y/2,/2) 475 12.3.3 EXPRESSION FOR THE POLYNOMIAL Q AO ,N(X) 476
12.3.4 EXPRESSION FOR THE POLYNOMIAL A0]N (X) 476 12.3.5 PROPERTIES OF
THE POLYNOMIAL $ A0I OO(XO,XI) 476 12.3.6 CONSTRUCTION OF THE CONSTANT
TERM N P AO (A) 477 12.3.7 CONSTRUCTION OF THE POLYNOMIAL Q AO ,N(X) 477
12.3.8 THE POLYNOMIAL $ AOJ00 (X O ,XI) 477 12.3.9 COMPUTATION OF THE
COEFFICIENTS OF THE POLYNOMIAL /A O ,OO(Z) 477 13 EXTENSIONS OF THE
CONSTRAINED NUMBERS 481 13.1 COMPARISON TO THE DIVIDED DIFFERENCE METHOD
481 13.1.1 COMPARISON 481 13.1.2 EXAMPLE 482 13.2 GENERALIZATION TO THE
SET OF POSITIVE REAL NUMBERS 483 13.3 CONSTRAINED COORDINATE SYSTEM WITH
MATRICES 485 14 FIELD OF THE COMPLEX NUMBERS 487 14.1 GENERALIZATION TO
THE FIELD OF THE COMPLEX NUMBERS 487 14.2 GENERATION OF THE POLYNOMIAL
A0) O(X) RELATED TO THE REFERENCE NODE DO = * 1 * I 488 14.2.1 ELEMENTS
COMMON TO ALL POLYNOMIALS RELATED TO THE NODE D 0 = (-1 -I) . 488
14.2.2 GENERATION OF THE POLYNOMIAL $ A0I O(X) RELATED TO THE REFERENCE
NODE AO = * 1 * I 490 14.2.3 COMPUTATION OF THE COEFFICIENTS OF THE
POLYNOMIAL /AOOOOC) 491 14.2.4 POLYNOMIALS RELATED TO THE NODE *1 * I
496 14.3 POLYNOMIAL $ AII0 (X) RELATED TO THE REFERENCE NODE A = L*I
497 14.4 POLYNOMIAL $ A2:0 (X) RELATED TO THE REFERENCE NODE A 2 = -1 +
I 498 14.5 POLYNOMIAL 3 A3I O(X) RELATED TO THE REFERENCE NODE A 3 = 1
+ I 498 15 ANALYSIS OF THE BEHAVIOR OF THE HERMITE INTERPOLATING POLY-
NOMIALS 499 15.1 ONE DIMENSIONAL HERMITE INTERPOLATING POLYNOMIALS . . .
. 499 15.1.1 THE SET OF FUNCTIONS 499 15.2 GRAPHICAL REPRESENTATION OF
THE HERMITE INTERPOLATING POLYNOMIALS $ A FN(X) FOR R * 4 . . . 501
15.2.1 GRAPHIC OF & A ,O(X) AND ITS DERIVATIVES 501 15.2.2 GRAPHIC OF $
A ,I(X) AND ITS DERIVATIVES 502 15.2.3 GRAPHIC OF THE POLYNOMIAL & A
,2(X) AND ITS DERIVATIVES 502 15.2.4 GRAPHIC OF $ TT) 3(X) AND ITS
DERIVATIVES 504 15.2.5 GRAPHIC OF THE POLYNOMIAL $ U] 4(X) AND ITS
DERIVATIVES 504 15.3 GRAPHIC OF POLYNOMIALS $I^N(X),N = 0,1,2, 3,4 505
15.3.1 GRAPHIC OF POLYNOMIALS $ A N(X),N = 0,1,2,3,4 .... 505 15.3.2
GRAPHIC OF POLYNOMIALS $I^(X),N = 0,1,2,3,4 . . . . 506 15.3.3 GRAPHIC
OF THE POLYNOMIALS $! 2 ^(X), N = 0,1,2,3,4 . . 506 15.3.4 GRAPHIC OF
THE POLYNOMIALS $I^N(X), N = 0,1,2,3,4 . . 507 15.3.5 GRAPHIC OF THE
POLYNOMIALS $^0*0, N = 0,1, 2,3,4 . . 508 15.3.6 GRAPHIC OF THE
POLYNOMIALS $ A ,I(X), I = 0, 3,..., 27 . . 508 15.3.7 GRAPHIC OF THE
FIRST DERIVATIVES OF THE POLYNOMIALS *I](X),I = 3,6,...,27 509 15.3.8
GRAPHIC OF THE SECOND DERIVATIVES OF THE POLYNOMIALS $I](X),I =
3,6,...,27 509 15.4 GRAPHICAL REPRESENTATION OF THE HERMITE
INTERPOLATING POLYNOMIALS $ M ,L(X) AND ^ W FOR N = 0,1,2,3,4 509
15.4.1 GRAPHIC OF THE POLYNOMIALS $II(X) AND $ B L(X) FOR N =
0,L,2,3,4 . 510 15.4.2 GRAPHIC OF THE POLYNOMIALS $A, N ( X ) AND $ 6
N(X) FOR N = 0,L,2,3,4 . 511 15.4.3 GRAPHIC OF THE POLYNOMIALS $A, N
(X) AND $ B2 ^(X) FOR N = 0,L,2,3,4 ! 513 15.4.4 GRAPHIC OF THE
POLYNOMIALS $I,(X) AND ^^(X) FOR N = 0,L,2,3,4 . 514 15.4.5 GRAPHIC OF
THE POLYNOMIALS $I,N(X) AND $ 6 ^(X) FOR N = 0,1,2,3,4 . 516 15.5
ONE-DIMENSIONAL MODIFIED HERMITE INTERPOLATING POLYNOMIALS 517 15.5.1
THE SET OF FUNCTIONS 517 15.6 ANALYSIS OF THE ERROR FOR SELECTED DEGREES
OF/E JN (D,X) . . . . 521 15.6.1 APPROXIMATION TO A LINE 521 15.7
SELECTED EXAMPLES OF HERMITE INTERPOLATING POLYNOMIALS . . . 523 15.7.1
ONE-DIMENSIONAL HERMITE INTERPOLATING POLYNOMIAL . . 523 15.7.2
TWO-DIMENSIONAL HERMITE INTERPOLATING POLYNOMIAL. . 523 15.7.3
THREE-DIMENSIONAL HERMITE INTERPOLATING POLYNOMIAL . 524 15.7.4 SUMMARY
OF THE POLYNOMIALS $^* 7 J NI N2;) RELATED TO THE NODE A E =
(-1,-1,-1) 524 15.7.5 SUMMARY OF THE POLYNOMIALS $^J N N2 RE I A ^
E( J ^ 0 ^Q NODE A E = (*1, * 1, * 1) AND 77 = 4 527 15.7.6
FOUR-DIMENSIONAL HERMITE INTERPOLATING POLYNOMIAL . 532 15.7.7 SUMMARY
OF THE POLYNOMIALS § FI NI N2 TL3 RELATED TO THE NODE A E = (*1,
* 1, * 1, * 1) AND 77 = 3 532 III SELECTED APPLICATIONS 535 16
CONSTRUCTION OF THE APPROXIMATE SOLUTION 537 16.1 ONE-DIMENSIONAL
PROBLEMS 537 16.1.1 SOLUTION EXPANDED IN TERMS OF THE HERMITE
INTERPOLATING POLYNOMIALS 537 16.1.2 COORDINATE TRANSFORMATION 538
16.1.3 ONE-DIMENSIONAL BOUNDARY CONDITIONS 540 16.2 HIGHER-DIMENSIONAL
PROBLEMS 540 16.2.1 ANALYSIS OF THE BOUNDARY CONDITIONS 540 16.2.2
REPRESENTATION OF A TWO-VARIABLE POLYNOMIAL ON ANY BA- SIS 542 16.2.3
REPRESENTATION OF A THREE-VARIABLE POLYNOMIAL ON ANY BASIS 543 16.2.4
EXAMPLE OF A THREE-VARIABLE POLYNOMIAL ON A CHEBYSHEV BASIS 544 16.2.5
EXAMPLE OF THE TWO-DIMENSIONAL SINE FUNCTION 545 16.2.6 THE POLYNOMIAL
APPROXIMATION 546 16.2.7 COMPUTATION OF THE COEFFICIENTS OF THE
EXPANSION OF THE SOLUTION 547 16.3 RESIDUAL ANALYSIS 548 16.3.1 RESIDUAL
ANALYSIS OF THE GOVERNING EQUATION 548 16.3.2 RESIDUAL ANALYSIS OF THE
SOLUTION 548 16.3.3 RESIDUAL ANALYSIS IN THE DOMAIN 549 16.4 COMMENTS
ABOUT THE COMPUTER PROGRAM 549 17 ONE-DIMENSIONAL TWO-POINT BOUNDARY
VALUE PROBLEMS 551 17.1 LINEAR DIFFERENTIAL EQUATION 551 17.1.1
APPROXIMATE SOLUTION IN THE DOMAIN [*0.5,0.5] . . . . 551 17.1.2
APPROXIMATE SOLUTION IN THE DOMAIN [*1,1] 555 17.1.3 ERROR ANALYSIS 559
17.2 NONLINEAR DIFFERENTIAL EQUATION 560 17.2.1 MODELING VISCOELASTIC
FLOWS: CASE I 560 17.2.2 MODELING VISCOELASTIC FLOWS: CASE II 569 17.2.3
ANALYSIS OF THE SOLUTION IN THE INTERVAL [*1,1] 578 17.3 FLOW OF
NON-NEWTONIAN FLUIDS: POWELL-EYRING MODEL 579 17.3.1 PRANDTL-EYRING
MODEL: CASE I 579 17.3.2 POWELL-EYRING MODEL: CASE II 583 17.4 TWO-POINT
BOUNDARY VALUE PROBLEM 586 17.4.1 SINGULAR PERTURBATION: PROBLEM I 586
17.4.2 SINGULAR PERTURBATION: PROBLEM II 596 17.4.3 SINGULAR
PERTURBATION: PROBLEM III 600 18 APPLICATION TO PROBLEMS WITH SEVERAL
VARIABLES 603 18.1 APPLICATION TO HEAT PROBLEMS 603 18.1.1 ONE-DIMENSION
HEAT FLOW EQUATION 603 18.1.2 TWO-DIMENSION HEAT FLOW EQUATION 605
18.1.3 TWO-DIMENSION HEAT FLOW EQUATION WITH LATERAL HEAT LOSS 606 18.2
APPLICATION TO THE WAVE EQUATION 608 18.2.1 HOMOGENEOUS ONE-DIMENSION
WAVE EQUATION 608 18.2.2 INHOMOGENEOUS ONE-DIMENSION WAVE EQUATION 609;
18.2.3 HOMOGENEOUS TWO-DIMENSION WAVE EQUATION 610 18.2.4 INHOMOGENEOUS
TWO-DIMENSION WAVE EQUATION 612 18.3 NONLINEAR PARTIAL DIFFERENTIAL
EQUATION 613 18.4 INHOMOGENEOUS ADVECTION EQUATION 614 19 THERMAL
ANALYSIS OF THE SURFACE OF THE SPACE SHUTTLE 617 19.1 PHYSICAL MODEL 617
19.1.1 THERMAL PROPERTIES 617 19.1.2 MATERIAL MODELING 618 19.1.3
PROPERTIES OF THE REMAINING LAYERS 621 19.1.4 HEAT GENERATED AT THE
EXTERNAL SURFACE 622 19.1.5 GEOMETRY 622 19.1.6 TEMPERATURES 623 19.2
MATHEMATICAL MODEL . 623 19.2.1 NONLINEAR GOVERNING DIFFERENTIAL
EQUATIONS 623 19.2.2 LINEAR GOVERNING DIFFERENTIAL EQUATIONS 624 19.2.3
SUMMARY OF GOVERNING EQUATIONS 624 19.2.4 BOUNDARY CONDITIONS 625 19.3
CONSTRUCTION OF THE APPROXIMATE SOLUTION 628 19.3.1 TYPES OF SOLUTIONS
628 19.3.2 SECOND-ORDER DIFFERENTIAL EQUATION FORMULATION 630 19.3.3
FIRST-ORDER DIFFERENTIAL EQUATION FORMULATION 635 19.3.4 COMPUTATION OF
THE RESIDUAL OF THE DIFFERENTIAL EQUATION 636 19.4 NUMERICAL COMPUTATION
636 19.5 ANALYSIS OF THE SOLUTIONS 640 19.5.1 GOVERNING EQUATION
RESIDUAL ANALYSIS 640 19.5.2 TWO-TEMPERATURE BOUNDARY CONDITION
APPROXIMATE SO- LUTION 641 19.5.3 HEAT-FLUX AND TEMPERATURE BOUNDARY
CONDITION . . . . 643 19.5.4 FIRST-ORDER DIFFERENTIAL GOVERNING EQUATION
645 19.6 TEMPERATURE DISTRIBUTION 649 19.7 COEFFICIENTS FOR THE
APPROXIMATE SOLUTION 651 19.7.1 POWER SERIES, CASE 1 DEGREE 15 651
19.7.2 CHEBYSHEV POLYNOMIAL, CASE 1 DEGREE 15 652 19.7.3 POWER SERIES,
CASE 7 DEGREE 15 652 19.7.4 CHEBYSHEV POLYNOMIAL, CASE 7 DEGREE 15 653
19.7.5 POWER SERIES, CASE 8 DEGREE 15 653 19.7.6 CHEBYSHEV POLYNOMIAL,
CASE 8 DEGREE 15 654 19.7.7 POWER SERIES, CASE 9 DEGREE 15 654 19.7.8
CHEBYSHEV POLYNOMIAL, CASE 9 DEGREE 15 655 19.8 CONCLUSION 656
REFERENCES 659 INDEX 663
|
| any_adam_object | 1 |
| author | Tavares, Santiago Alves |
| author_GND | (DE-588)137922124 |
| author_facet | Tavares, Santiago Alves |
| author_role | aut |
| author_sort | Tavares, Santiago Alves |
| author_variant | s a t sa sat |
| building | Verbundindex |
| bvnumber | BV026753690 |
| classification_rvk | SK 680 |
| ctrlnum | (OCoLC)634650001 (DE-599)HBZHT014517339 |
| dewey-full | 515.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.55 |
| dewey-search | 515.55 |
| dewey-sort | 3515.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01549nam a2200397 cb4500</leader><controlfield tag="001">BV026753690</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20210601 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110326s2006 d||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">GBA572182</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1584885726</subfield><subfield code="9">1-584-88572-6</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781584885726</subfield><subfield code="9">978-1-584-88572-6</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)634650001</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)HBZHT014517339</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-188</subfield><subfield code="a">DE-83</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515.55</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 680</subfield><subfield code="0">(DE-625)143252:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">41A05</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">41A63</subfield><subfield code="2">msc</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Tavares, Santiago Alves</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)137922124</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Generation of multivariate Hermite interpolating polynomials</subfield><subfield code="c">Santiago Alves Tavares, University of Florida, Gainesville, FL, U.S.A.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Boca Raton, Fla. [u.a.]</subfield><subfield code="b">Chapman & Hall/CRC</subfield><subfield code="c">2006</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">672 Seiten</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Pure and Applied Mathematics</subfield><subfield code="v">274</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hermite polynomials</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multivariate analysis</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Pure and Applied Mathematics</subfield><subfield code="v">274</subfield><subfield code="w">(DE-604)BV000001885</subfield><subfield code="9">274</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022290876&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-022290876</subfield></datafield></record></collection> |
| id | DE-604.BV026753690 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:18:23Z |
| institution | BVB |
| isbn | 1584885726 9781584885726 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022290876 |
| oclc_num | 634650001 |
| open_access_boolean | |
| owner | DE-188 DE-83 |
| owner_facet | DE-188 DE-83 |
| physical | 672 Seiten graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Pure and Applied Mathematics |
| series2 | Pure and Applied Mathematics |
| spelling | Tavares, Santiago Alves Verfasser (DE-588)137922124 aut Generation of multivariate Hermite interpolating polynomials Santiago Alves Tavares, University of Florida, Gainesville, FL, U.S.A. Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2006 672 Seiten graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and Applied Mathematics 274 Includes bibliographical references and index Hermite polynomials Multivariate analysis Pure and Applied Mathematics 274 (DE-604)BV000001885 274 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022290876&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tavares, Santiago Alves Generation of multivariate Hermite interpolating polynomials Pure and Applied Mathematics Hermite polynomials Multivariate analysis |
| title | Generation of multivariate Hermite interpolating polynomials |
| title_auth | Generation of multivariate Hermite interpolating polynomials |
| title_exact_search | Generation of multivariate Hermite interpolating polynomials |
| title_full | Generation of multivariate Hermite interpolating polynomials Santiago Alves Tavares, University of Florida, Gainesville, FL, U.S.A. |
| title_fullStr | Generation of multivariate Hermite interpolating polynomials Santiago Alves Tavares, University of Florida, Gainesville, FL, U.S.A. |
| title_full_unstemmed | Generation of multivariate Hermite interpolating polynomials Santiago Alves Tavares, University of Florida, Gainesville, FL, U.S.A. |
| title_short | Generation of multivariate Hermite interpolating polynomials |
| title_sort | generation of multivariate hermite interpolating polynomials |
| topic | Hermite polynomials Multivariate analysis |
| topic_facet | Hermite polynomials Multivariate analysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022290876&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000001885 |
| work_keys_str_mv | AT tavaressantiagoalves generationofmultivariatehermiteinterpolatingpolynomials |