Applications of linear and nonlinear models: fixed effects, random effects, and total least squares
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
2012
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| Schriftenreihe: | Springer geophysics
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| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturangaben. - Hergestellt on demand |
| Beschreibung: | XXI, 1016 S. graph. Darst. 24 cm |
| ISBN: | 9783642222405 3642222404 |
Internformat
MARC
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| 100 | 1 | |a Grafarend, Erik W. |d 1939-2020 |e Verfasser |0 (DE-588)121959368 |4 aut | |
| 245 | 1 | 0 | |a Applications of linear and nonlinear models |b fixed effects, random effects, and total least squares |c Erik W. Grafarend ; Joseph L. Awange |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c 2012 | |
| 300 | |a XXI, 1016 S. |b graph. Darst. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Springer geophysics | |
| 500 | |a Literaturangaben. - Hergestellt on demand | ||
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| 856 | 4 | 2 | |m X:MVB |q text/html |u http://deposit.dnb.de/cgi-bin/dokserv?id=3835654&prov=M&dok_var=1&dok_ext=htm |3 Inhaltstext |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025424433 | |
Datensatz im Suchindex
| _version_ | 1807954437467013120 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
1 THE FIRST PROBLEM O F ALGEBRAIC REGRESSION {AX = Y | A E M " X M , Y E
7(A) ~ RK A = = D I M ) , MINOS . . . . 1
1-1 INTRODUCTION 4
1-11 THE FRONT PAGE EXAMPLE 5
1-12 THE FRONT PAGE EXAMPLE: MATRIX ALGEBRA 5
1-13 THE FRONT PAGE EXAMPLE: MINOS, HORIZONTAL RANK PARTITIONING 8
1-14 THE RANGE 7 1 ( F ) AND THE KERNEL A F ( F ) 10
1-15 THE INTERPRETATION O F MINOS 12
1-2 MINIMUM NORM SOLUTION (MINOS) 16
1-21 A DISCUSSION O F THE METRIC O F THE PARAMETER SPACE X 21
1-22 AN ALTERNATIVE CHOICE O F THE METRIC O F THE PARAMETER SPACE X 22
1 -23 G X - M I N O S AND ITS GENERALIZED INVERSE 22
1-24 EIGENVALUE DECOMPOSITION OF G V -MINOS: CANONICAL MINOS 2 4
1-3 CASE STUDY 37
1-31 FOURIER SERIES 38
1-32 FOURIER-LEGENDRE SERIES 4 9
1-33 NYQUIST FREQUENCY FOR SPHERICAL DATA 62
1-4 - SPECIAL NONLINEAR MODELS 63
1-41 TAYLOR POLYNOMIALS, GENERALIZED NEWTON ITERATION 63
1-42 LINEARIZED MODELS WITH DATUM DEFECT 69
1-5 NOTES 78
XIII
HTTP://D-NB.INFO/101246282X
IMAGE 2
X I V C O N T E N T S
2 THE FIRST PROBLEM O F PROBABILISTIC REGRESSION:
THE BIAS PROBLEM SPECIAL GAUSS-MARKOV MODEL WITH DATUM DEFECTS, LUMBE 81
2-1 LINEAR UNIFORMLY MINIMUM BIAS ESTIMATOR (LUMBE) 84
2-2 THE EQUIVALENCE THEOREM O F G X -MLNOS AND S-LUMBE 87
2-3 EXAMPLE 88
3 THE SECOND PROBLEM O F ALGEBRAIC REGRESSION INCONSISTENT SYSTEM O F
LINEAR OBSERVATIONAL EQUATIONS 89
3-1 INTRODUCTION 92
3-11 THE FRONT PAGE EXAMPLE 92
3-12 THE FRONT PAGE EXAMPLE IN MATRIX ALGEBRA 9 3
3-13 LEAST SQUARES SOLUTION O F THE FRONT PAGE EXAMPLE BY MEANS OF
VERTICAL RANK PARTITIONING 95
3-14 THE RANGE 7 Z ( F ) AND THE KERNEL M ( F ) ,
INTERPRETATION O F "LESS" BY THREE PARTITIONINGS 98
3-2 THE LEAST SQUARES SOLUTION: "LESS" 105
3-21 A DISCUSSION O F THE METRIC O F THE PARAMETER SPACE X 112
3-22 ALTERNATIVE CHOICES OF THE METRIC OF THE OBSERVATION 113
3-23 GX-LESS AND ITS GENERALIZED INVERSE 129
3-24 EIGENVALUE DECOMPOSITION O F G Y -LESS: CANONICAL LESS 130
3-3 CASE STUDY 141
3-31 CANONICAL ANALYSIS OF THE HAT MATRIX, PARTIAL REDUNDANCIES, HIGH
LEVERAGE POINTS 142
3-32 MULTILINEAR ALGEBRA, "JOIN" AND "MEET", THE HODGE STAR OPERATOR 150
3-33 FROM A TO B: LATENT RESTRICTIONS, GRASSMANN COORDINATES, PLIICKER
COORDINATES 156
3-34 FROM B TO A: LATENT PARAMETRIC EQUATIONS, DUAL GRASSMANN
COORDINATES, DUAL PLIICKER COORDINATES 168
3-35 BREAKPOINTS 172
3-4 SPECIAL LINEAR AND NONLINEAR MODELS: A FAMILY OF MEANS FOR DIRECT
OBSERVATIONS 180
3-5 A HISTORICAL NOTE ON C.F. GAUSS AND A.M. LEGENDRE 180
4 THE SECOND PROBLEM O F PROBABILISTIC REGRESSION SPECIAL GAUSS-MARKOV
MODEL WITHOUT DATUM DEFECT 183
4-1 INTRODUCTION 187
4-11 THE FRONT PAGE EXAMPLE 188
4-12 ESTIMATORS OF TYPE BLUUE AND BIQUUE OF THE FRONT PAGE EXAMPLE 189
IMAGE 3
CONTENTS X V
4-13 BLUUE AND BIQUUE O F THE FRONT PAGE
EXAMPLE, SAMPLE MEDIAN, MEDIAN ABSOLUTE DEVIATION 198
4-14 ALTERNATIVE ESTIMATION MAXIMUM LIKELIHOOD (MALE) 202
4-2 SETUP O F THE BEST LINEAR UNIFORMLY UNBIASED ESTIMATOR 205
4-21 THE BEST LINEAR UNIFORMLY UNBIASED ESTIMATION § OF : E Y -BLUUE
206
4-22 THE EQUIVALENCE THEOREM O F G Y -LESS AND E Y -BLUUE 213
4-3 SETUP O F THE BEST INVARIANT QUADRATIC UNIFORMLY UNBIASED ESTIMATOR
214
4-31 BLOCK PARTITIONING OF THE DISPERSION MATRIX AND LINEAR SPACE
GENERATED BY VARIANCE-COVARIANCE COMPONENTS 215
4-32 INVARIANT QUADRATIC ESTIMATION OF VARIANCE-COVARIANCE COMPONENTS O
F TYPE IQE 220
4-33 INVARIANT QUADRATIC UNIFORMLY UNBIASED ESTIMATIONS O F
VARIANCE-COVARIANCE COMPONENTS O F TYPE IQUUE 224
4-34 INVARIANT QUADRATIC UNIFORMLY UNBIASED ESTIMATIONS O F ONE VARIANCE
COMPONENT (IQUUE) FROM E Y -BLUUE: HIQUUE 228
4-35 INVARIANT QUADRATIC UNIFORMLY UNBIASED ESTIMATORS O F VARIANCE
COVARIANCE COMPONENTS O F HELMERT TYPE: HIQUUE VERSUS HIQE 230
4-36 BEST QUADRATIC UNIFORMLY UNBIASED ESTIMATIONS O F ONE VARIANCE
COMPONENT: BIQUUE 234 4-37 SIMULTANEOUS DETERMINATION O F FIRST MOMENT
AND THE SECOND CENTRAL MOMENT,
INHOMOGENEOUS MULTILINEAR ESTIMATION, THE E - D CORRESPONDENCE, BAYES
DESIGN WITH MOMENT ESTIMATIONS 241
5 THE THIRD PROBLEM O F ALGEBRAIC REGRESSION (AX + I = Y | A E M " X M ,
Y N (A) ~ R K A MIN{W, N}} 263
5-1 INTRODUCTION 265
5-11 THE FRONT PAGE EXAMPLE 266
5-12 THE FRONT PAGE EXAMPLE IN MATRIX ALGEBRA 266
5-13 MINIMUM NORM: LEAST SQUARES SOLUTION OF THE FRONT PAGE EXAMPLE BY
MEANS OF ADDITIVE RANK PARTITIONING 268
IMAGE 4
X V I C O N T E N T S
5-14 MINIMUM NORM: LEAST SQUARES SOLUTION
O F THE FRONT PAGE EXAMPLE BY MEANS OF MULTIPLICATIVE RANK PARTITIONING
272
5-15 THE RANGE R(F) AND THE KERNEL N(F) INTERPRETATION O F "MINOLESS" BY
THREE PARTITIONINGS 276
5-2 MINOLESS AND RELATED SOLUTIONS LIKE WEIGHTED MINIMUM NORM-WEIGHTED
LEAST SQUARES SOLUTIONS 283
5-21 THE MINIMUM NORM-LEAST SQUARES SOLUTION: "MINOLESS" 283
5-22 (G X , G Y )-MINOS AND ITS GENERALIZED INVERSE 293
5-23 EIGENVALUE DECOMPOSITION OF (G X , G Y )-MINOLESS 297
5-24 NOTES 301
5-3 THE HYBRID APPROXIMATION SOLUTION: A - H A P S AND TYKHONOV-PHILLIPS
REGULARIZATION 302
6 THE THIRD PROBLEM O F PROBABILISTIC REGRESSION SPECIAL GAUSS-MARKOV
MODEL WITH DATUM DEFECT 305
6-1 SETUP O F THE BEST LINEAR MINIMUM BIAS ESTIMATOR OF TYPE BLUMBE 308
6-11 DEFINITIONS, LEMMAS AND THEOREMS 310
6-12 THE FIRST EXAMPLE: BLUMBE VERSUS BLE, BIQUUE VERSUS BIQE,
TRIANGULAR LEVELING NETWORK 317
6-2 SETUP O F THE BEST LINEAR ESTIMATORS OF TYPE HORN BLE, HORN S-BLE
AND HOM A-BLE FOR FIXED EFFECTS 332
6-3 CONTINUOUS NETWORKS 345
6-31 CONTINUOUS NETWORKS O F SECOND DERIVATIVES TYPE 346
6-32 DISCRETE VERSUS CONTINUOUS GEODETIC NETWORKS 357
7 OVERDETERMINED SYSTEM O F NONLINEAR EQUATIONS ON CURVED MANIFOLDS
INCONSISTENT SYSTEM O F DIRECTIONAL OBSERVATIONAL EQUATIONS 361 7-1
INTRODUCTION 362
7-2 MINIMAL GEODESIC DISTANCE: MINGEODISC 365
7-3 SPECIAL MODELS: FROM THE CIRCULAR NORMAL DISTRIBUTION TO THE OBLIQUE
NORMAL DISTRIBUTION 370
7-31 A HISTORICAL NOTE O F THE VON MISES DISTRIBUTION 370
7-32 OBLIQUE MAP PROJECTION 372
7-33 A NOTE ON THE ANGULAR METRIC 375
7-4 CASE STUDY 376
IMAGE 5
CONTENTS X V I I
8 THE FOURTH PROBLEM O F PROBABILISTIC REGRESSION
SPECIAL GAUSS-MARKOV MODEL WITH RANDOM EFFECTS 383
8-1 THE RANDOM EFFECT MODEL 384
8-2 EXAMPLES 399
9 THE FIFTH PROBLEM O F ALGEBRAIC REGRESSION: THE SYSTEM O F CONDITIONAL
EQUATIONS: HOMOGENEOUS AND INHOMOGENEOUS EQUATIONS: {BY = BI VERSUS -C +
BY = BI} 411
9-1 GY -LESS O F A SYSTEM O F A INCONSISTENT HOMOGENEOUS CONDITIONAL
EQUATIONS 411
9-2 SOLVING A SYSTEM OF INCONSISTENT INHOMOGENEOUS CONDITIONAL EQUATIONS
415
9-3 EXAMPLES 416
10 THE FIFTH PROBLEM O F PROBABILISTIC REGRESSION GENERAL GAUSS-MARKOV
MODEL WITH MIXED EFFECTS 419
10-1 INHOMOGENEOUS GENERAL LINEAR GAUSS-MARKOV MODEL FIXED EFFECTS AND
RANDOM EFFECTS 421
10-2 EXPLICIT REPRESENTATIONS O F ERRORS IN THE GENERAL GAUSS-MARKOV
MODEL WITH MIXED EFFECTS 426
10-3 AN EXAMPLE FOR COLLOCATION 428
10-4 COMMENTS 438
11 THE SIXTH PROBLEM OF PROBABILISTIC REGRESSION - THE RANDOM EFFECT
MODEL - "ERRORS-IN-VARIABLE" 443
11-1 THE MODEL O F ERROR-IN-VARIABLES OR TOTAL LEAST SQUARES 447
11-2 ALGEBRAIC TOTAL LEAST SQUARES FOR THE NONLINEAR SYSTEM O F THE
MODEL "ERROR-IN-VARIABLES" 448
11-3 EXAMPLE: THE STRAIGHT LINE FIT 450
11-4 THE MODELS SIMEX AND SYMEX 453
11-5 REFERENCES 459
12 THE NONLINEAR PROBLEM O F THE 3D DATUM TRANSFORMATION AND THE
PROCRUSTES ALGORITHM 461
12-1 THE 3D DATUM TRANSFORMATION AND THE PROCRUSTES ALGORITHM . 463
12-2 THE VARIANCE: COVARIANCE MATRIX O F THE ERROR MATRIX E 470
12-21 CASE STUDIES: THE 3D DATUM TRANSFORMATION AND THE PROCRUSTES
ALGORITHM 471
12-3 REFERENCES 474
13 THE SIXTH PROBLEM O F GENERALIZED ALGEBRAIC REGRESSION THE SYSTEM O F
CONDITIONAL EQUATIONS WITH UNKNOWNS - (GAUSS-HELMERT MODEL) 477
13-1 VARIANCE-COVARIANCE-COMPONENT ESTIMATION IN THE LINEAR MODEL AX + S
= Y, Y 71(A) 479
13-2 VARIANCE-COVARIANCE-COMPONENT ESTIMATION IN THE LINEAR MODEL BE =
BY - C, BY 7Z(A) + C 482
IMAGE 6
X V I I I C O N T E N T S
13-3 VARIANCE-COVARIANCE-COMPONENT ESTIMATION IN THE
LINEAR MODEL AX 4- S + BE = BY - C, BY ^ 71(A) + C 485
13-4 THE BLOCK STRUCTURE O F DISPERSION MATRIX D{Y} 489
14 SPECIAL PROBLEMS O F ALGEBRAIC REGRESSION AND STOCHASTIC ESTIMATION
493
14-1 THE MULTIVARIATE GAUSS-MARKOV MODEL: A SPECIAL PROBLEM O F
PROBABILISTIC REGRESSION 4 9 3
14-2 N-WAY CLASSIFICATION MODELS 498
14-21 A FIRST EXAMPLE: 1-WAY CLASSIFICATION 499
14-22 A SECOND EXAMPLE: 2-WAY CLASSIFICATION WITHOUT INTERACTION 503
14-23 A THIRD EXAMPLE: 2-WAY CLASSIFICATION WITH INTERACTION 509
14-24 HIGHER CLASSIFICATIONS WITH INTERACTION 514
14-3 DYNAMICAL SYSTEMS 517
15 ALGEBRAIC SOLUTIONS O F SYSTEMS O F EQUATIONS LINEAR AND NONLINEAR
SYSTEMS O F EQUATIONS 527
15-1 INTRODUCTORY REMARKS 527
15-2 BACKGROUND TO ALGEBRAIC SOLUTIONS 528
15-3 ALGEBRAIC METHODS FOR SOLVING NONLINEAR SYSTEMS O F EQUATIONS 532
15-31 SOLUTION OF NONLINEAR GAUSS-MARKOV MODEL 532
15-32 ADJUSTMENT OF THE COMBINATORIAL SUBSETS 552
15-4 EXAMPLES 556
15-5 NOTES 563
A TENSOR ALGEBRA, LINEAR ALGEBRA, MATRIX ALGEBRA, MULTILINEAR ALGEBRA
571
A-1 MULTILINEAR FUNCTIONS AND THE TENSOR SPACE 572
A-2 DECOMPOSITION O F MULTILINEAR FUNCTIONS INTO SYMMETRIC MULTILINEAR
FUNCTIONS ANTISYMMETRIC MULTI-LINEAR FUNCTIONS AND RESIDUAL MULTILINEAR
FUNCTIONS TTQ = 8 % AG 578
A-3 MATRIX ALGEBRA, ARRAY ALGEBRA, MATRIX NORM AND INNER PRODUCT 584
A-4 THE HODGE STAR OPERATOR, SELF DUALITY 587
A-5 LINEAR ALGEBRA 592
A-51 DEFINITION O F A LINEAR ALGEBRA 593
A-52 THE DIAGRAMS "ASS", "UNI" AND "COMM" 595
A-53 RINGED SPACES: THE SUBALGEBRA "RING WITH IDENTITY" 597
A-54 DEFINITION OF A DIVISION ALGEBRA AND NON-ASSOCIATIVE ALGEBRA 598
IMAGE 7
CONTENTS X I X
A-55 LIE ALGEBRA, WITT ALGEBRA 598
A-56 DEFINITION OF A COMPOSITION ALGEBRA 599
A-6 MATRIX ALGEBRA REVISITED, GENERALIZED INVERSES 602
A-61 SPECIAL MATRICES: HELMERT MATRIX, HANKEL MATRIX, VANDEMONTE MATRIX
606
A-62 SCALAR MEASURES OF MATRICES 612
A-63 THREE BASIC TYPES O F GENERALIZED INVERSES 618
A-7 COMPLEX ALGEBRA, QUATERNION ALGEBRA, OCTONIAN ALGEBRA, CLIFFORD
ALGEBRA, HURWITZ THEOREM 619
A-71 COMPLEX ALGEBRA AS A DIVISION ALGEBRA AS WELL AS A COMPOSITION
ALGEBRA, CLIFFORD ALGEBRA C L ( 0 , 1) 620
A-72 QUATERNION ALGEBRA AS A DIVISION ALGEBRA AS WELL AS A COMPOSITION
ALGEBRA, CLIFFORD ALGEBRA C 1(0,2) 622
A-73 OCTANIAN ALGEBRA AS A NON-ASSOCIATIVE ALGEBRA AS WELL AS A
COMPOSITION ALGEBRA, CLIFFORD ALGEBRA WITH RESPECT T O I X L 629
A-74 CLIFFORD ALGEBRA 633
B SAMPLING DISTRIBUTIONS AND THEIR USE: CONFIDENCE INTERVALS AND
CONFIDENCE REGIONS 637
B-L A FIRST VEHICLE: TRANSFORMATION O F RANDOM VARIABLES 638
B-2 A SECOND VEHICLE: TRANSFORMATION O F RANDOM VARIABLES 642
B-3 A FIRST CONFIDENCE INTERVAL OF GAUSS-LAPLACE NORMALLY DISTRIBUTED
OBSERVATIONS FI, A 2 KNOWN, THE THREE SIGMA RULE 648
B-31 THE FORWARD COMPUTATION O F A FIRST CONFIDENCE INTERVAL O F
GAUSS-LAPLACE NORMALLY DISTRIBUTED OBSERVATIONS: FI, A 2 KNOWN 653
B-32 THE BACKWARD COMPUTATION O F A FIRST CONFIDENCE INTERVAL O F
GAUSS-LAPLACE NORMALLY DISTRIBUTED OBSERVATIONS: \I, A 2 KNOWN 659 B-4
SAMPLING FROM THE G A U S S -
LAPLACE NORMAL DISTRIBUTION: A SECOND CONFIDENCE INTERVAL FOR THE MEAN,
VARIANCE KNOWN 662
B-41 SAMPLING DISTRIBUTIONS O F THE SAMPLE MEAN JX, A 2 KNOWN, AND O F
THE SAMPLE VARIANCE A 2 677
B-42 THE CONFIDENCE INTERVAL FOR THE SAMPLE MEAN, VARIANCE KNOWN 688
B-5 SAMPLING FROM THE GAUSS- LAPLACE NORMAL DISTRIBUTION: A THIRD
CONFIDENCE INTERVAL FOR THE MEAN, VARIANCE UNKNOWN 692
B-51 STUDENT'S SAMPLING DISTRIBUTION O F THE RANDOM VARIABLE (FT - F I )
/ O 692
IMAGE 8
X X
C O N T E N T S
B-52 THE CONFIDENCE INTERVAL FOR THE MEAN,
VARIANCE UNKNOWN 701
B-53 THE UNCERTAINTY PRINCIPLE 707
B-6 SAMPLING FROM THE G A U S S - LAPLACE NORMAL DISTRIBUTION: A FOURTH
CONFIDENCE INTERVAL FOR THE VARIANCE 708
B-61 THE CONFIDENCE INTERVAL FOR THE VARIANCE 709
B-62 THE UNCERTAINTY PRINCIPLE 715
B-7 SAMPLING FROM THE MULTIDIMENSIONAL GAUSS-LAPLACE NORMAL
DISTRIBUTION: THE CONFIDENCE REGION FOR THE FIXED PARAMETERS IN THE
LINEAR GAUSS-MARKOV MODEL 717
B-8 MULTIDIMENSIONAL VARIANCE ANALYSIS, SAMPLING FROM THE MULTIVARIATE
GAUSS-LAPLACE NORMAL DISTRIBUTION 739
B-81 DISTRIBUTION O F SAMPLE MEAN AND VARIANCE-COVARIANCE 740
B-82 DISTRIBUTION RELATED TO CORRELATION COEFFICIENTS 744
C STATISTICAL NOTIONS, RANDOM EVENTS AND STOCHASTIC PROCESSES 753 C-L
MOMENTS OF A PROBABILITY DISTRIBUTION, THE G A U S S LAPLACE NORMAL
DISTRIBUTION AND THE QUASI-NORMAL DISTRIBUTION 754
C-2 ERROR PROPAGATION 757
C-3 USEFUL IDENTITIES 760
C-4 SCALAR - VALUED STOCHASTIC PROCESSES OF ONE PARAMETER 762
C-5 CHARACTERISTIC O F ONE PARAMETER STOCHASTIC PROCESSES 765
C-6 SIMPLE EXAMPLES O F ONE PARAMETER STOCHASTIC PROCESSES 769
C - L WIENER PROCESSES 781
C-71 DEFINITION O F THE WIENER PROCESSES 781
C-72 SPECIAL WIENER PROCESSES: ORNSTEIN- UHLENBECK, WIENER PROCESSES
WITH DRIFT, INTEGRAL WIENER PROCESSES 785
C-8 SPECIAL ANALYSIS O F ONE PARAMETER STATIONARY STOCHASTIC PROCESS 793
C-81 FOUNDATIONS: ERGODIC AND STATIONARY PROCESSES 793
C-82 PROCESSES WITH DISCRETE SPECTRUM 795
* C-83 PROCESSES WITH CONTINUOUS SPECTRUM 798
C-84 SPECTRAL DECOMPOSITION O F THE MEAN AND VARIANCE-COVARIANCE
FUNCTION 808
C-9 SCALAR-, VECTOR-, AND TENSOR VALUED STOCHASTIC PROCESSES O F
MULTI-PARAMETER SYSTEMS 811
C-91 CHARACTERISTIC FUNCTIONAL 812
C-92 THE MOMENT REPRESENTATION OF STOCHASTIC PROCESSES FOR SCALAR VALUED
AND VECTOR VALUED QUANTITIES 814
C-93 TENSOR-VALUED STATISTICAL HOMOGENEOUS AND ISOTROPIC FIELD OF
MULTI-POINT SYSTEMS 818
IMAGE 9
CONTENTS X X I
D BASICS O F GROEBNER BASIS ALGEBRA 887
D-L DEFINITIONS 887
D-2 BUCHBERGER ALGORITHM 889
D-21 MATHEMATICA COMPUTATION OF GROEBNER BASIS 889
D-22 MAPLE COMPUTATION O F GROEBNER BASIS 891
D.3 GAUSS COMBINATORIAL FORMULATION . 892
REFERENCES 895
INDEX 1011 |
| any_adam_object | 1 |
| author | Grafarend, Erik W. 1939-2020 Awange, Joseph L. 1969- |
| author_GND | (DE-588)121959368 (DE-588)123537959 |
| author_facet | Grafarend, Erik W. 1939-2020 Awange, Joseph L. 1969- |
| author_role | aut aut |
| author_sort | Grafarend, Erik W. 1939-2020 |
| author_variant | e w g ew ewg j l a jl jla |
| building | Verbundindex |
| bvnumber | BV040596598 |
| classification_rvk | SK 840 |
| ctrlnum | (OCoLC)812568602 (DE-599)DNB101246282X |
| dewey-full | 519.536 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.536 |
| dewey-search | 519.536 |
| dewey-sort | 3519.536 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040596598 |
| illustrated | Illustrated |
| indexdate | 2024-08-21T00:21:50Z |
| institution | BVB |
| isbn | 9783642222405 3642222404 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025424433 |
| oclc_num | 812568602 |
| open_access_boolean | |
| owner | DE-859 |
| owner_facet | DE-859 |
| physical | XXI, 1016 S. graph. Darst. 24 cm |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer geophysics |
| spelling | Grafarend, Erik W. 1939-2020 Verfasser (DE-588)121959368 aut Applications of linear and nonlinear models fixed effects, random effects, and total least squares Erik W. Grafarend ; Joseph L. Awange Berlin ; Heidelberg Springer 2012 XXI, 1016 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Springer geophysics Literaturangaben. - Hergestellt on demand Lineares Regressionsmodell (DE-588)4127971-2 gnd rswk-swf Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd rswk-swf Lineares Regressionsmodell (DE-588)4127971-2 s Nichtlineares Regressionsmodell (DE-588)4251078-8 s DE-604 Awange, Joseph L. 1969- Verfasser (DE-588)123537959 aut X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3835654&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025424433&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Grafarend, Erik W. 1939-2020 Awange, Joseph L. 1969- Applications of linear and nonlinear models fixed effects, random effects, and total least squares Lineares Regressionsmodell (DE-588)4127971-2 gnd Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd |
| subject_GND | (DE-588)4127971-2 (DE-588)4251078-8 |
| title | Applications of linear and nonlinear models fixed effects, random effects, and total least squares |
| title_auth | Applications of linear and nonlinear models fixed effects, random effects, and total least squares |
| title_exact_search | Applications of linear and nonlinear models fixed effects, random effects, and total least squares |
| title_full | Applications of linear and nonlinear models fixed effects, random effects, and total least squares Erik W. Grafarend ; Joseph L. Awange |
| title_fullStr | Applications of linear and nonlinear models fixed effects, random effects, and total least squares Erik W. Grafarend ; Joseph L. Awange |
| title_full_unstemmed | Applications of linear and nonlinear models fixed effects, random effects, and total least squares Erik W. Grafarend ; Joseph L. Awange |
| title_short | Applications of linear and nonlinear models |
| title_sort | applications of linear and nonlinear models fixed effects random effects and total least squares |
| title_sub | fixed effects, random effects, and total least squares |
| topic | Lineares Regressionsmodell (DE-588)4127971-2 gnd Nichtlineares Regressionsmodell (DE-588)4251078-8 gnd |
| topic_facet | Lineares Regressionsmodell Nichtlineares Regressionsmodell |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3835654&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025424433&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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