Numerical analysis: an introduction
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Boston
De Gruyter
[2019]
|
| Series: | De Gruyter Graduate
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 175 Seiten Diagramme (teilweise farbig) |
| ISBN: | 9783110573305 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV045455455 | ||
| 003 | DE-604 | ||
| 005 | 20230508 | ||
| 007 | t | ||
| 008 | 190212s2019 gw |||| |||| 00||| eng d | ||
| 015 | |a 18,N41 |2 dnb | ||
| 016 | 7 | |a 1168253691 |2 DE-101 | |
| 020 | |a 9783110573305 |c pbk. |9 978-3-11-057330-5 | ||
| 035 | |a (OCoLC)1090776086 | ||
| 035 | |a (DE-599)DNB1168253691 | ||
| 040 | |a DE-604 |b ger |e rda | ||
| 041 | 0 | |a eng | |
| 044 | |a gw |c XA-DE-BE | ||
| 049 | |a DE-20 |a DE-1050 |a DE-706 |a DE-19 |a DE-703 |a DE-634 |a DE-83 |a DE-11 | ||
| 084 | |a SK 900 |0 (DE-625)143268: |2 rvk | ||
| 084 | |a 65-01 |2 msc | ||
| 084 | |a 510 |2 sdnb | ||
| 100 | 1 | |a Heister, Timo |d 1983- |0 (DE-588)1183011571 |4 aut | |
| 245 | 1 | 0 | |a Numerical analysis |b an introduction |c Timo Heister ; Leo G. Rebholz and Fei Xue |
| 264 | 1 | |a Berlin ; Boston |b De Gruyter |c [2019] | |
| 264 | 4 | |c © 2019 | |
| 300 | |a XVII, 175 Seiten |b Diagramme (teilweise farbig) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a De Gruyter Graduate | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 653 | |a Fachhochschul-/Hochschulausbildung | ||
| 653 | |a Fachhochschul-/Hochschulausbildung | ||
| 653 | |a Finite-Differenzen-Methode | ||
| 653 | |a MATLAB | ||
| 653 | |a Numerische Mathematik | ||
| 689 | 0 | 0 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Rebholz, Leo G. |0 (DE-588)1020166274 |4 aut | |
| 700 | 1 | |a Xue, Fei |0 (DE-588)143680803 |4 aut | |
| 710 | 2 | |a Walter de Gruyter GmbH & Co. KG |0 (DE-588)10095502-2 |4 pbl | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, PDF |z 978-3-11-057332-9 |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe, EPUB |z 978-3-11-057333-6 |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030840759&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-030840759 | ||
Record in the Search Index
| _version_ | 1804179357073145856 |
|---|---|
| adam_text | CONTENTS
PREFACE
*
VII
SOFTWARE
*
IX
ACKNOWLEDGMENT
*
XI
SUPPORT
*
XIII
1
1.1
1.2
1.3
1.3.1
1.3.2
1.4
COMPUTER
REPRESENTATION
OF
NUMBERS
AND
ROUNDOFF
ERROR
*
1
EXAMPLES
OF
THE
EFFECTS
OF
ROUNDOFF
ERROR
*
1
BINARY
NUMBERS
-----
4
64
BIT
FLOATING-POINT
NUMBERS
*
6
ADDING
LARGE
AND
SMALL
NUMBERS
IS
BAD
*
8
SUBTRACTING
TWO
NEARLY
EQUAL
NUMBERS
IS
BAD
*
8
EXERCISES
*
10
2
2.1
2.2
2.3
2.3.1
2.4
2.5
2.6
2.7
2.7.1
2.7.2
2.7.3
2.7.4
2.8
SOLVING
LINEAR
SYSTEMS
OF
EQUATIONS
*
13
SOLVING
TRIANGULAR
LINEAR
SYSTEMS
*
13
FROM
GAUSSIAN
ELIMINATION
TO
LU
FACTORIZATION
*
15
PIVOTING
-----
18
WORKINLU/GE
-----
23
DIRECT
METHODS
FOR
LARGE
SPARSE
LINEAR
SYSTEMS
*
23
CONJUGATE
GRADIENT
*
26
PRECONDITIONING
AND
ILU
-----
28
ACCURACY
IN
SOLVING
LINEAR
SYSTEMS
*
30
MATRIX
AND
VECTOR
NORMS
AND
CONDITION
NUMBER
*
31
CONDITION
NUMBER
OF
A
MATRIX
*
33
SENSITIVITY
IN
LINEAR
SYSTEM
SOLVING
*
34
ERROR
AND
RESIDUAL
IN
LINEAR
SYSTEM
SOLVING
*
36
EXERCISES-----
37
3
3.1
3.2
3.3
3.4
LEAST
SQUARES
PROBLEMS
*
41
SOLVING
LSQ
PROBLEMS
WITH
THE
NORMAL
EQUATIONS
*
42
QR
FACTORIZATION
AND
THE
GRAM-SCHMIDT
PROCESS
*
44
CURVE
OF
BEST
FIT
-----
48
EXERCISES
*
51
4
4.1
FINITE
DIFFERENCE
METHODS
*
53
CONVERGENCE
TERMINOLOGY
*
53
XVI
*
CONTENTS
4.2
4.2.1
4.2.2
4.2.3
4.2.4
4.3
4.4
4.5
4.6
APPROXIMATING
THE
FIRST
DERIVATIVE
*
55
FORWARD
AND
BACKWARD
DIFFERENCES
*
55
CENTERED
DIFFERENCE
*
58
THREE
POINT
DIFFERENCE
FORMULAS
*
60
FURTHER
NOTES
-----62
APPROXIMATING
THE
SECOND
DERIVATIVE
*
62
APPLICATION:
INITIAL
VALUE
ODES
USING
THE
FORWARD
EULER
METHOD
*
63
APPLICATION:
BOUNDARY
VALUE
ODES
*
65
EXERCISES
*
69
5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
SOLVING
NONLINEAR
EQUATIONS
*
71
CONVERGENCE
CRITERIA
OF
ITERATIVE
METHODS
FOR
NONLINEAR
SYSTEMS
*
71
THE
BISECTION
METHOD
*
72
FIXED-POINT
THEORY
AND
ALGORITHMS
*
77
NEWTON
*
S
METHOD
*
82
SECANT
METHOD
*
86
COMPARING
BISECTION,
NEWTON,
SECANT
METHOD
*
86
COMBINING
SECANT
AND
BISECTION
AND
THE
FZERO
COMMAND
*
87
EQUATION
SOLVING
IN
HIGHER
DIMENSIONS
*
87
EXERCISES
*
90
6
6.1
6.2
6.3
6.4
6.5
EIGENVALUES
AND
EIGENVECTORS
*
93
THEORETICAL
BACKGROUND
*
93
SINGLE-VECTOR
ITERATIONS
*
94
MULTIPLE-VECTOR
ITERATIONS
*
101
FINDING
ALL
EIGENVALUES
AND
EIGENVECTORS
OF
A
MATRIX
*
103
EXERCISES
*
103
7
7.1
7.1.1
7.2
7.3
7.4
7.5
INTERPOLATION
*
105
INTERPOLATION
BY
A
SINGLE
POLYNOMIAL
*
105
LAGRANGE
INTERPOLATION
*
107
CHEBYSHEV
INTERPOLATION
*
110
PIECEWISE
LINEAR
INTERPOLATION
*
113
PIECEWISE
CUBIC
INTERPOLATION
(CUBIC
SPLINE)
*
116
EXERCISES
*
119
8
8.1
8.2
8.3
8.4
8.5
NUMERICAL
INTEGRATION
*
121
PRELIMINARIES
*
121
NEWTON-COTES
RULES
*
124
COMPOSITE
RULES
-----
127
CLENSHAW-CURTIS
QUADRATURE
*
130
GAUSS
QUADRATURE
*
133
CONTENTS
*
XVII
8.6
MATLAB
*
S
INTEGRAL
FUNCTION
-----
138
8.7
EXERCISE-----
139
9
INITIAL
VALUE
PROBLEMS
*
141
9.1
REDUCTION
OF
HIGHER
ORDER
IVPS
TO
FIRST
ORDER
*
142
9.2
THE
FORWARD
EULER
METHOD
-----
143
9.3
HEUN
*
S
METHOD
AND
RK4
-----
146
9.4
STIFF
PROBLEMS
AND
NUMERICAL
STABILITY
*
147
9.4.1
IMPLICIT
METHODS
AND
UNCONDITIONAL
STABILITY
*
149
9.5
SUMMARY,
GENERAL
STRATEGY,
AND
MATLAB
ODE
SOLVERS
-----
150
9.6
FITTING
ODE
PARAMETERS
TO
DATA
*
152
9.7
EXERCISES-----
155
10
PARTIAL
DIFFERENTIAL
EQUATIONS
*
159
10.1
THE
ID
HEAT
EQUATION
*
159
10.1.1
A
MAXIMUM
PRINCIPLE
AND
NUMERICAL
STABILITY
*
166
10.2
THE
2D
POISSON
EQUATION
*
168
10.3
EXERCISES
*
172
INDEX
*
173
|
| any_adam_object | 1 |
| author | Heister, Timo 1983- Rebholz, Leo G. Xue, Fei |
| author_GND | (DE-588)1183011571 (DE-588)1020166274 (DE-588)143680803 |
| author_facet | Heister, Timo 1983- Rebholz, Leo G. Xue, Fei |
| author_role | aut aut aut |
| author_sort | Heister, Timo 1983- |
| author_variant | t h th l g r lg lgr f x fx |
| building | Verbundindex |
| bvnumber | BV045455455 |
| classification_rvk | SK 900 |
| ctrlnum | (OCoLC)1090776086 (DE-599)DNB1168253691 |
| discipline | Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02023nam a2200517 c 4500</leader><controlfield tag="001">BV045455455</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230508 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">190212s2019 gw |||| |||| 00||| eng d</controlfield><datafield tag="015" ind1=" " ind2=" "><subfield code="a">18,N41</subfield><subfield code="2">dnb</subfield></datafield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1168253691</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110573305</subfield><subfield code="c">pbk.</subfield><subfield code="9">978-3-11-057330-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1090776086</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1168253691</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">gw</subfield><subfield code="c">XA-DE-BE</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-20</subfield><subfield code="a">DE-1050</subfield><subfield code="a">DE-706</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 900</subfield><subfield code="0">(DE-625)143268:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">65-01</subfield><subfield code="2">msc</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">510</subfield><subfield code="2">sdnb</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Heister, Timo</subfield><subfield code="d">1983-</subfield><subfield code="0">(DE-588)1183011571</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Numerical analysis</subfield><subfield code="b">an introduction</subfield><subfield code="c">Timo Heister ; Leo G. Rebholz and Fei Xue</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Berlin ; Boston</subfield><subfield code="b">De Gruyter</subfield><subfield code="c">[2019]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2019</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVII, 175 Seiten</subfield><subfield code="b">Diagramme (teilweise farbig)</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="0" ind2=" "><subfield code="a">De Gruyter Graduate</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerische Mathematik</subfield><subfield code="0">(DE-588)4042805-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fachhochschul-/Hochschulausbildung</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Fachhochschul-/Hochschulausbildung</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Finite-Differenzen-Methode</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">MATLAB</subfield></datafield><datafield tag="653" ind1=" " ind2=" "><subfield code="a">Numerische Mathematik</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Numerische Mathematik</subfield><subfield code="0">(DE-588)4042805-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Rebholz, Leo G.</subfield><subfield code="0">(DE-588)1020166274</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Xue, Fei</subfield><subfield code="0">(DE-588)143680803</subfield><subfield code="4">aut</subfield></datafield><datafield tag="710" ind1="2" ind2=" "><subfield code="a">Walter de Gruyter GmbH & Co. KG</subfield><subfield code="0">(DE-588)10095502-2</subfield><subfield code="4">pbl</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, PDF</subfield><subfield code="z">978-3-11-057332-9</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe, EPUB</subfield><subfield code="z">978-3-11-057333-6</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB 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=030840759&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:BVB01-030840759</subfield></datafield></record></collection> |
| id | DE-604.BV045455455 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:18:34Z |
| institution | BVB |
| institution_GND | (DE-588)10095502-2 |
| isbn | 9783110573305 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030840759 |
| oclc_num | 1090776086 |
| open_access_boolean | |
| owner | DE-20 DE-1050 DE-706 DE-19 DE-BY-UBM DE-703 DE-634 DE-83 DE-11 |
| owner_facet | DE-20 DE-1050 DE-706 DE-19 DE-BY-UBM DE-703 DE-634 DE-83 DE-11 |
| physical | XVII, 175 Seiten Diagramme (teilweise farbig) |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | De Gruyter |
| record_format | marc |
| series2 | De Gruyter Graduate |
| spelling | Heister, Timo 1983- (DE-588)1183011571 aut Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue Berlin ; Boston De Gruyter [2019] © 2019 XVII, 175 Seiten Diagramme (teilweise farbig) txt rdacontent n rdamedia nc rdacarrier De Gruyter Graduate Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Fachhochschul-/Hochschulausbildung Finite-Differenzen-Methode MATLAB Numerische Mathematik Numerische Mathematik (DE-588)4042805-9 s DE-604 Rebholz, Leo G. (DE-588)1020166274 aut Xue, Fei (DE-588)143680803 aut Walter de Gruyter GmbH & Co. KG (DE-588)10095502-2 pbl Erscheint auch als Online-Ausgabe, PDF 978-3-11-057332-9 Erscheint auch als Online-Ausgabe, EPUB 978-3-11-057333-6 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030840759&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Heister, Timo 1983- Rebholz, Leo G. Xue, Fei Numerical analysis an introduction Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical analysis an introduction |
| title_auth | Numerical analysis an introduction |
| title_exact_search | Numerical analysis an introduction |
| title_full | Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue |
| title_fullStr | Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue |
| title_full_unstemmed | Numerical analysis an introduction Timo Heister ; Leo G. Rebholz and Fei Xue |
| title_short | Numerical analysis |
| title_sort | numerical analysis an introduction |
| title_sub | an introduction |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030840759&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT heistertimo numericalanalysisanintroduction AT rebholzleog numericalanalysisanintroduction AT xuefei numericalanalysisanintroduction AT walterdegruytergmbhcokg numericalanalysisanintroduction |