Theory of linear algebraic equations with random coefficients:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Allerton Press
1996
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXIV, 320 S. |
| ISBN: | 0898640784 |
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| 100 | 1 | |a Girko, Vʼjačeslav Leonidovyč |d 1946- |e Verfasser |0 (DE-588)1055764976 |4 aut | |
| 245 | 1 | 0 | |a Theory of linear algebraic equations with random coefficients |c Vyacheslav L. Girko |
| 264 | 1 | |a New York |b Allerton Press |c 1996 | |
| 300 | |a XXIV, 320 S. | ||
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| 650 | 7 | |a Lineaire algebra |2 gtt | |
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| 650 | 7 | |a Multivariate analyse |2 gtt | |
| 650 | 4 | |a Equations |x Numerical solutions | |
| 650 | 4 | |a Random variables | |
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Record in the Search Index
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| adam_text | THEORY OF LINEAR ALGEBRAIC EQUATIONS WITH RANDOM COEFFICIENTS VYACHESLAV
L. GIRKO AUERTON PRESS, INC./NEW YORK CONTENTS LIST OF BASIC NOTATIONS
AND ASSUMPTIONS XIII INTRODUCTION XVI CHAPTER 1. SPECTRAL THEORY OF
ESTIMATING PARAMETERS OF A SYSTEM OF LINEAR EQUATIONS 1 1. PERTURBATION
FORMULAS FOR EIGENVALUES AND EIGENVECTORS OF MATRIX 2 2. THEOREM ON THE
EXTREMAL VALUES OF BOUNDED FUNCTION 3 3. THE MAIN SPECTRAL EQUATION. THE
METHOD OF RANDOM MATRIX REGULARIZATION 5 4. THE CLASSICAL LEAST SQUARES
METHOD 8 5. SPECTRAL EQUATION SI FOR MINIMAX ESTIMATORS OF PARAMETERS IN
LINEAR MODELS 9 6. LINEAR MODELS WITH UNKNOWN COVARIANCE MATRIX.
SPECTRAL EQUATION 52 17 7. LINEAR MODELS WITH NONRANDOM PERTURBATIONS.
SPECTRAL EQUATION 53 17 8. SPECTRAL EQUATION 5 4 FOR THE ESTIMATORS OF
THE SOLUTIONS OF SYSTEMS OF EQUATIONS WITH INTERNAL PERTURBATIONS IN A
SYSTEM OF OBSERVATIONS 18 9. LINEAR MODELS WITH AN ARBITRARY SET OF
PERTURBATIONS. SPECTRAL EQUATION S 5 20 10. ESTIMATION OF STATES/OF SOME
RECURSIVELY DEFINED SYSTEMS 22 11. ESTIMATION OF DYNAMIC SYSTEM STATES
24 12. ESTIMATION OF LINEAR REGRESSION MODELS IN HILBERT SPACE 27
CHAPTER 2. DETERMINAN T CONDITIONS FOR THE EXISTENCE OF SOLUTIONS OF
SLAERC 30 1. FORMULATION OF THE PROBLEM 30 2. LIMIT THEOREM FOR THE SUM
OF MARTINGALE DIFFERENCES 31 3. LIMIT THEOREM OF THE TYPE OF LARGE
NUMBERS LAW FOR RANDOM DETERMINANTS 31 4. THE CENTRAL LIMIT THEOREM FOR
RANDOM DETERMINANTS 32 5. THE METHOD OF PERPENDICULARS 35 6. RESOLVENT
FORMULAS FOR MATRIX WITH INDEPENDENT PAIRS OF ITS ENTRIES 36 7. THE
THEOREM OF THE TYPE OF LARGE NUMBERS LAW AND THE CENTRAL LIMIT THEOREM
FOR DETERMINANT OF RANDOM GRAM MATRIX 37 8. METHOD OF NORMAL RANDOM
REGULARIZATION FOR DETERMINANTS 40 9. LOGARITHMIC LAW FOR RANDOM
DETERMINANTS 43 10. LOGARITHMIC LAW FOR RANDOM DETERMINANTS WITH SMALL
ERRORS IN ENTRIES 46 VI CONTENTS CHAPTER 3. DISTRIBUTION FUNCTION OF
SOLUTION OF SLAERC AND INTEGRAL REPRESENTATION METHOD 50 1. RANDOM
CONDITION NUMBER 50 2. SLAERC WITH NORMALLY DISTRIBUTED COEFFICIENTS 51
3. DISTRIBUTION OF EIGENVALUES AND EIGENVECTORS OF RANDOM MATRICES 51 4.
SPECTRAL METHOD FOR THE CALCULATION OF MOMENTS FOR SOLUTIONS OF SLAERC
52 5. THE STOCHASTIC LEAST SQUARES METHOD 53 6. ARCTANGENT LAW 53 7.
STOCHASTIC LEONTIEF MODEL 54 8. INTEGRAL REPRESENTATION FOR DETERMINANTS
54 9. LIMIT THEOREM FOR RANDOM DETERMINANTS 54 10. INTEGRAL
REPRESENTATION METHOD FOR SOLUTIONS OF SLAERC 55 11. INTEGRAL
REPRESENTATION FOR SOLUTIONS OF DIFFERENTIAL EQUATIONS OF THE SECOND
ORDER 56 12. SIMULATION IN LINEAR ALGEBRA 56 CHAPTER 4. THE SPECTRAL
CONDITIONS FOR THE EXISTENCE AND BOUNDEDNESS OF THE SOLUTIONS OF SLAERC
WITH LARGE DIMENSION 59 1. CANONICAL EQUATION C 5 FOR G-DENSITY AND L5
EQUATION FOR THE BOUNDARY POINTS OF G-DENSITY 59 2. CANONICAL EQUATION.
LIMIT THEOREM FOR NORMALIZED SPECTRAL FUNCTIONS 67 3. THE REFORM METHOD
OF DERIVING THE MAIN EQUATION OF SPECTRAL THEORY OF RANDOM MATRICES 70
4. INEQUALITIES FOR THE COEFFICIENTS OF THE MAIN EQUATION 72 5.
CALCULATIONS OF COEFFICIENTS OF THE MAIN EQUATION 75 6. INVARIANCE
PRINCIPLE FOR RANDOM MATRICES . 77 7. EQUATION FOR THE SUM OF SMOOTHED
DISTRIBUTION FUNCTIONS OF SINGULAR VALUES OF RANDOM MATRICES 81 8. THE
METHOD OF FOURIER AND INVERSE FOURIER TRANSFORMS FOR FINDING BOUNDARIES
OF EIGENVALUES 82 9. RANDOM PERTURBATION METHOD FOR THE EIGENVALUES 88
10. LIMIT THEOREM FOR THE SINGULAR VALUES OF RANDOM MATRICES 88 11.
CANONICAL SPECTRAL EQUATION AND L 4 EQUATION FOR THE BOUNDARY POINTS OF
THE SPECTRAL DENSITY OF SYMMETRIC RANDOM MATRICES 91 12. LIMIT THEOREM
FOR EIGENVALUES OF RANDOM SYMMETRIC MATRICES 92 13. CONDITIONS FOR THE
EXISTENCE AND BOUNDEDNESS OF THE SOLUTIONS OF SLAERC OF LARGE DIMENSION
93 * 14. SPECTRAL CONDITIONS FOR THE EXISTENCE OF SLAERC SOLUTIONS 94
CHAPTER 5. THE CIRCULAR, ELLIPTIC, AND UNIFORM LAWS AND V-DENSITY FOR
THE EIGENVALUES OF RANDOM MATRICES 95 1. OUTLINE OF THE PROOF OF
CIRCULAR AND ELLIPTIC LAWS (GIRKO, 1985) 95 CONTENTS VII 2. SPECTRAL AND
G-FUNCTIONS 97 3. GENERAL ^-TRANSFORM OF SPECTRAL FUNCTIONS 98 4.
TRUNCATED V -TRANSFORM AND ^-TRANSFORM 99 5. CONDITIONAL V^-TRANSFORM
AND V^-TRANSFORM 101 6. CANONICAL SPECTRAL EQUATION AND L 5 EQUATION FOR
THE BOUNDARY POINTS OF SPECTRAL DENSITY 102 7. CANONICAL EQUATION. LIMIT
THEOREMS FOR SPECTRAL SINGULAR FUNCTIONS 105 8. THE REFORM METHOD OF
DERIVING THE MAIN EQUATION OF THE SPECTRAL THEORY OF A RANDOM MATRIX 108
9. INEQUALITIES FOR THE COEFFICIENTS OF THE MAIN EQUATION 110 10.
CALCULATIONS OF COEFFICIENTS OF THE MAIN EQUATION 113 11. IN VARIANCE
PRINCIPLE FOR RANDOM MATRICES 115 12. THE EQUATION FOR THE SUM OF
SMOOTHED DISTRIBUTION FUNCTIONS OF EIGENVALUES OF RANDOM MATRICES 119
13. THE METHOD OF FOURIER AND INVERSE FOURIER TRANSFORMS FOR FINDING
BOUNDARIES OF EIGENVALUES 120 14. LIMIT THEOREM FOR THE SINGULAR VALUES
OF RANDOM MATRICES 122 15. THE METHOD OF PERPENDICULARS FOR PROVING THE
CIRCULAR LAW 122 16. CENTRAL LIMIT THEOREM FOR RANDOMLY NORMALIZED
RANDOM DETERMINANTS 123 17. SUBSTITUTION OF NORMALLY DISTRIBUTED RANDOM
VARIABLES FOR THE ENTRIES OF RANDOM MATRICES 125 18. SUBSTITUTION OF THE
DETERMINANT OF GRAM MATRIX FOR THE DETERMINANT OF MATRIX 126 19.
REGULARIZED VS-TRANSFORM 129 20. CALCULATION OF A CERTAIN INTEGRAL 130
21. LIMIT THEOREM FOR FOURIER TRANSFORMS OF SPECTRAL FUNCTIONS AND
NORMALIZED REGULARIZED RANDOM DETERMINANTS 131 22. INVERSE FORMULA FOR
THE STIELTJES TRANSFORM OF LIMIT SPECTRAL FUNCTION OF NON-SELF-ADJOINT
RANDOM MATRICES 132 23. REGULARIZED V 6 -TRANSFORM. THE CIRCULAR LAW 133
24. LIMIT THEOREMS FOR THE EIGENVALUES OF RANDOM MATRICES WITH
INDEPENDENT ENTRIES 134 25. THE ELLIPTIC LAW 136 26. LIMIT THEOREMS FOR
THE EIGENVALUES OF RANDOM NONSYMMETRIC MATRICES 137 27. THE V-DENSITY OF
EIGENVALUES OF RANDOM MATRICES WITH INDEPENDENT PAIRS OF ENTRIES 137 28.
THE V-DENSITY OF EIGENVALUES OF RANDOM MATRICES WITH INDEPENDENT ENTRIES
139 29. EXAMPLES OF THE G-REGION OF V-DENSITY FOR EIGENVALUES OF RANDOM
MATRICES WITH INDEPENDENT ENTRIES 139 VIII CONTENTS CHAPTER 6. CANONICAL
EQUATION FOR THE SOLUTIONS OF A SYSTEM OF LINEAR ALGEBRAIC EQUATIONS
WITH INDEPENDENT RANDOM COEFFICIENTS 146 1. FORMULATION OF THE PROBLEM
147 2. THE COMPLEX REGULARIZATION AND INTEGRO-DIFFERENTIAL
REPRESENTATION FOR SOLUTIONS OF SLAE 147 3. REFORM METHOD 148 4. LIMIT
THEOREMS FOR ENTRIES OF THE RESOLVENT OF RANDOM MATRICES 149 5. ANALYTIC
CONTINUATION OF ENTRIES OF RESOLVENTS 155 6. CALCULATION OF THE
DERIVATIVE OF A RESOLVENT OF A RANDOM MATRIX 155 7. THE MAIN ASSERTION
156 8. THE CANONICAL EQUATION 157 9. THE SLAERC WITH SPECIAL STRUCTURE
OF A MATRIX OF COEFFICIENTS 160 10. CANONICAL EQUATION FOR THE SOLUTION
OF SLAERC WHOSE COEFFICIENTS HAVE IDENTITY VARIANCES 162 CHAPTER 7.
SYSTEM OF LINEAR ALGEBRAIC EQUATIONS WITH SYMMETRIC BLOCK MATRIX
STRUCTURE 165 1. FORMULATION OF THE PROBLEM 165 2. BLOCK MATRICES 166 3.
REFORM METHOD. FORMULA FOR DIAGONAL BLOCKS OF RESOLVENT 167 4. REFORM
METHOD. PERTURBATION FORMULAS FOR BLOCKS OF SYMMETRIC MATRICES 168 5.
THE BOUNDEDNESS OF NORMS OF RESOLVENT BLOCKS 169 6. LIMIT THEOREM FOR
RANDOM MATRIX POLYNOMIAL FUNCTIONS OF THE SECOND ORDER 169 7. LIMIT
THEOREMS FOR THE SOLUTION OF SLAERC WITH INDEPENDENT SYMMETRIC BLOCK
STRUCTURE / 172 8. THE CANONICAL EQUATION FOR RANDOM BLOCK MATRICES 175
9. CANONICAL EQUATION FOR THE SOLUTION OF SLAERC WITH INDEPENDENT
SYMMETRIC BLOCK STRUCTURE 176 10. EXAMPLES 177 CHAPTER 8. CANONICAL
EQUATION FOR SLAERC WITH NONSYMMETRIC BLOCK MATRIX OF COEFFICIENTS 181
1,. NONSYMMETRIC BLOCK MATRICES 181 2. REFORM METHOD. FORMULA FOR BLOCKS
OF GRAM MATRIX 182 3. INEQUALITY FOR RANDOM QUADRATIC FORMS 184 4. LIMIT
THEOREMS FOR SOLUTIONS OF SLAERG WITH INDEPENDENT RANDOM BLOCK STRUCTURE
184 5. ANALYTIC CONTINUATION OF ENTRIES OF RESOLVENTS 187 6. THE
CANONICAL EQUATION FOR RANDOM BLOCK MATRICES 187 7. CANONICAL EQUATION
FOR SLAERC WITH BLOCK STRUCTURE 188 CONTENTS IX CHAPTER 9. SYSTEM OF
LINEAR ALGEBRAIC EQUATIONS WITH ASYMPTOTICALLY INDEPENDENT SYMMETRIC
BLOCKS 191 1. FORMULATION OF THE PROBLEM. 191 2. METHOD OF THINNING
MATRICES: BLOCK MATRICES 192 3. THE G-CONDITION OF ASYMPTOTIC
INDEPENDENCE OF BLOCKS OF SYMMETRIC RANDOM MATRICES 192 4. METHOD OF
SHORTENING ENTRIES OF BLOCKS OF RANDOM MATRICES 193 5. LIMIT THEOREMS
FOR QUADRATIC FORMS OF ASYMPTOTICALLY INDEPENDENT RANDOM BLOCKS 195 6.
THE M-CONDITION OF ASYMPTOTIC INDEPENDENCE OF RANDOM BLOCKS 197 7. LIMIT
THEOREMS FOR THE SOLUTION OF SLAERC WITH ASYMPTOTICALLY INDEPENDENT
SYMMETRIC BLOCKS STRUCTURE 197 CHAPTER 10. THE CANONICAL EQUATION FOR
SOLUTIONS OF SLAERC WITH NONSYMMETRIC MATRIX OF ASYMPTOTICALLY
INDEPENDENT RANDOM COEFFICIENTS 199 1. FORMULATION OF THE PROBLEM 199 2.
METHOD OF THINNING MATRICES: BLOCK MATRICES 200 3. THE CONDITION OF
ASYMPTOTIC INDEPENDENCE OF BLOCKS OF RANDOM MATRICES 200 4. LIMIT
THEOREMS FOR QUADRATIC FORMS OF ASYMPTOTICALLY INDEPENDENT RANDOM BLOCKS
201 5. LIMIT THEOREMS FOR SOLUTIONS OF SLAERC WITH AN ASYMPTOTICALLY
INDEPENDENT RANDOM BLOCK 204 6. CANONICAL EQUATION FOR SLAERC UNDER THE
AF-CONDITION 205 / CHAPTER 11. G-NORMAL STATISTICAL ESTIMATORS FOR
SOLUTIONS OF SLAE 206 1. FORMULATION OF THE PROBLEM AND GENERALIZED
G-CONDITION FOR SLAERC 206 2. INTEGRAL REPRESENTATION FOR THE
G-ESTIMATOR OF THE SOLUTION OF SLAE 207 3. MARTINGALE REPRESENTATION FOR
THE SOLUTION OF SLAERC 208 4. SUBSTITUTION OF COEFFICIENTS OF SLAERC FOR
NORMALLY DISTRIBUTED RANDOM VARIABLES ; 209 5. SUBSTITUTION OF THE
SOLUTION OF SLAERC FOR A SOLUTION OF THE ACCOMPANYING CANONICAL EQUATION
210 6. CALCULATION OF THE PARTIAL DERIVATIVES FOR RESOLVENTS 211 7.
EXISTENCE OF SOLUTIONS OF THE MAIN EQUATION OF GS-ESTIMATOR 212 8. SOME
FORMULAS FOR THE DERIVATIVE OF THE RESOLVENT OF RANDOM MATRICES 213 9.
THE MAIN FORMULA FOR ESTIMATOR G% 213 10. LIMIT THEOREMS FOR RANDOM
QUADRATIC FORMS 214 11. CONVERGENCE OF A SOLUTION OF AN ACCOMPANYING
CANONICAL EQUATION TO THE SOLUTION OF A CANONICAL EQUATION 218 12. A
REPLACEMENT OF RANDOM SOLUTION 220 X CONTENTS 13. ASYMPTOTIC BEHAVIOUR
OF THE SUM OF MARTINGALE DIFFERENCES 222 14. INVARIANCE PRINCIPLE FOR
THE SOLUTION OF SLAERC 224 15. THE REPLACEMENT OF A CANONICAL EQUATION
FOR THE SOLUTION OF SLAERC 225 16. G8-ESTIMATOR WITH A COMPLEX
REGULARIZING PARAMETER 227 17. G-NORMAL ESTIMATOR FOR THE SOLUTIONS OF
SLAE WHEN OBSERVATIONS OF THE COEFFICIENTS HAVE EQUIVALENT VARIANCES 229
18. CONDITIONS FOR VANISHING OF A COMPLEX REGULARIZATOR 231 19. G-NORMAL
ESTIMATORS FOR SOLUTIONS OF SLAE WHEN OBSERVATIONS OF THE COEFFICIENTS
HAVE VARIANCES EQUAL TO THE PRODUCT OF SOME VALUES 233 CHAPTER 12.
GS-CONSISTENT ESTIMATORS FOR SOLUTIONS OF SLAE WITH BLOCK STRUCTURE 236
1. LIMIT THEOREMS FOR ENTRIES OF THE RESOLVENT OF RANDOM MATRICES 236 2.
SUBSTITUTION OF TRUNCATED BLOCK DIAGONAL MATRICES FOR BLOCK DIAGONAL
MATRICES 241 3. ANALYTIC CONTINUATION OF ENTRIES OF RESOLVENTS 242 4.
BOUNDEDNESS OF SOLUTIONS OF THE SYSTEM OF G-EQUATIONS 243 5. RANDOM
SUBSTITUTION OF BLOCK PARAMETERS 244 6. GS-ESTIMATOR FOR SOLUTIONS OF
SLAE WHEN OBSERVATIONS OFTHE COEFFICIENTS HAVE ARBITRARY VARIANCES 245
7. THE CONDITIONS FOR VANISHING PARAMETERS OF COMPLEX REGULARIZATION.
CONSISTENCY OF THE GS-ESTIMATOR 246 CHAPTER 13. GS-CONSISTENT ESTIMATORS
FOR SOLUTIONS OF SLAE WITH SYMMETRIC BLOCK STRUCTURE 250 1. FORMULATION
OF THE ESTIMATION PROBLEM FOR THE SOLUTION OF SLAE 250 2. LIMIT THEOREMS
FOR|ENTRIES OF THE RESOLVENT OF RANDOM MATRICES 251 3. SUBSTITUTION OF
TRUNCATED BLOCK DIAGONAL MATRICES FOR BLOCK DIAGONAL MATRICES 252 4.
ANALYTIC CONTINUATION OF ENTRIES OF RESOLVENTS 253 5. BOUNDEDNESS OF
SOLUTIONS OF THE SYSTEM OF G-EQUATIONS 253 6. RANDOM SUBSTITUTION OF
BLOCK PARAMETERS 254 7. G8-ESTIMATOR FOR SOLUTIONS OF SLAE WITH
SYMMETRIC BLOCK STRUCTURE WHEN OBSERVATIONS OF THE COEFFICIENTS HAVE
ARBITRARY VARIANCES 254 8. THE CONDITIONS FOR VANISHING PARAMETERS OF
COMPLEX REGULARIZATION. CONSISTENCY OF THE GS-ESTIMATOR 255 CHAPTER 14.
SELF-AVERAGING OF SOLUTIONS OF THE PROBLEMS OF LINEAR STOCHASTIC
PROGRAMMING OF LARGE DIMENSIONS 257 1. FORMULATION OF THE LINEAR
PROGRAMMING PROBLEM 257 2. FORMULATION OF THE LINEAR STOCHASTIC
PROGRAMMING PROBLEM 258 3. SOME ASPECTS OF GENERAL STATISTICAL ANALYSIS
258 4. SUBSTITUTION OF A SYSTEM OF LINEAR ALGEBRAIC EQUATIONS FOR THE
SYSTEM OF LINEAR INEQUALITIES 259 CONTENTS XI 5. ARCTANGENT LAW 259 6.
REGULARIZED FORM OF LSPP 260 7. THE DIFFICULTIES WITH RANDOM SOLUTIONS
OF LSPP WHEN REAL SOLUTIONS ARENONRANDOM 261 8. THE DIFFICULTIES WITH
RANDOM SOLUTIONS OF LSPP WHEN REAL SOLUTIONS ARE RANDOM 261 9.
SUBSTITUTION OF NONRANDOMLPP FOR LSPP 261 10. FORMULATION OF LSPP UNDER
CONDITIONS OF GENERAL STATISTICAL ANALYSIS 262 11. SYSTEMS OF LINEAR
ALGEBRAIC EQUATIONS WITH RANDOM COEFFICIENTS 262 12. LIMIT THEOREMS FOR
THE SINGULAR VALUES OF RANDOM MATRICES 264 13. SPECTRAL CONDITION FOR
LSPP 265 14. REFORM METHOD FOR LSPP WITH SYMMETRIC MATRIX A. CANONICAL
EQUATION AND CONSISTENT ESTIMATOR FOR SOLUTION OF LSPP 266 15. REFORM
METHOD FOR LSPP WITH NONSYMMETRIC MATRIX ^.CANONICAL EQUATION FOR LSPP
267 16. G-CONSISTENT ESTIMATOR FOR SOLUTIONS OF LSP 269 17. INTEGRAL
REPRESENTATION METHOD 270 18. CANONICAL EQUATION FOR LSPP WITH
INDEPENDENT BLOCK STRUCTURE 271 CHAPTER 15. STOCHASTIC KOLMOGOROV-WIENER
FILTER 273 1. CANONICAL EQUATION C AND EQUATION L FOR THE EXTREME
POINTS OF SPECTRAL DENSITY 274 2. SUBSTITUTION OF A NONRANDOM VECTOR FOR
THE VECTOR OF EMPIRICAL EXPECTATION 275 3. LIMIT THEOREM FOR NORMALIZED
SPECTRAL FUNCTIONS 276 4. INVARIANCE PRINCIPLE FOR THE EMPIRICAL
COVARIANCE MATRIX 277 5. EQUATION FOR THE SUM OF SMOOTHED DISTRIBUTION
FUNCTIONS OF EIGENVALUES OF EMPIRICAL COVARIANCE MATRICES 278 6. THE
MAIN ASSERTION. LIMIT THEOREM FOR EIGENVALUES OF THE EMPIRICAL
COVARIANCE MATRIX 279 7. G2-ESTIMATOR FOR THE STIELTJES TRANSFORM OF THE
NORMALIZED SPECTRAL FUNCTION OF COVARIANCE MATRICES 280 8. ASYMPTOTIC
NORMALITY OF THE G2-ESTIMATOR 281 9. SPECTRAL CONDITION FOR THE
EXISTENCE OF A SOLUTION OF THE KOLMOGOROV-WIENER FILTER 281 10. THE
CANONICAL EQUATION 282 11. THE METHOD OF SHORTENING ENTRIES OF EMPIRICAL
COVARIANCE MATRICES 283 12. SELF-AVERAGING OF RANDOM QUADRATIC FORMS 284
13. EXISTENCE AND UNIQUENESS OF A SOLUTION OF THE CONDITIONAL CANONICAL
EQUATION 286 14. EXISTENCE AND UNIQUENESS OF A SOLUTION OF THE CANONICAL
EQUATION 289 15. SUBSTITUTION OF A SOLUTION OF THE CONDITIONAL CANONICAL
EQUATION FOR AN EMPIRICAL COVARIANCE MATRIX 290 XII CONTENTS 16. PROOF
OF THE MAIN ASSERTION 291 17. EXAMPLES OF STOCHASTIC REGULARIZED
KOLMOGOROV-WIENER FILTERS 293 18. CONSISTENT ESTIMATOR FOR THE SOLUTION
OF THE REGULARIZED DISCRETE KOLMOGOROV-WIENER FILTER WITH KNOWN FREE
VECTOR 297 19. CONSISTENT ESTIMATOR FOR THE SOLUTION OF THE
KOLMOGOROV-WIENER FILTER WITH UNKNOWN FREE VECTOR 298 CHAPTER 16.
SELF-AVERAGING OF SOLUTIONS OF THE SYSTEM OF LINEAR DIFFERENTIAL
EQUATIONS WITH RANDOM COEFFICIENTS 303 1. SYSTEM OF LINEAR DIFFERENTIAL
EQUATIONS WITH RANDOM COEFFICIENTS 303 2. FORMULATION OF THE PROBLEM
UNDER THE CONDITIONS OF GENERAL STATISTICAL ANALYSIS 304 3. VI-TRANSFORM
OF THE SOLUTION OF THE SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS 304 4.
^-TRANSFORM OF THE SOLUTION OF THE SYSTEM OF LINEAR DIFFERENTIAL
EQUATIONS 305 5. V3-TRANSFORM OF THE SOLUTION OF THE SYSTEM OF LINEAR
DIFFERENTIAL EQUATIONS 306 6. LIMIT THEOREM FOR SINGULAR VALUES OF
RANDOM COMPLEX MATRICES 307 7. LIMIT THEOREM FOR V-TRANSFORMS OF THE
SOLUTION OF THE SYSTEM OF LINEAR DIFFERENTIAL EQUATIONS 307 8. VANISHING
OF RANDOM COEFFICIENTS OF A SYSTEM OF DIFFERENTIAL EQUATIONS 308
REFERENCES 310 INDEX 318
|
| any_adam_object | 1 |
| author | Girko, Vʼjačeslav Leonidovyč 1946- |
| author_GND | (DE-588)1055764976 |
| author_facet | Girko, Vʼjačeslav Leonidovyč 1946- |
| author_role | aut |
| author_sort | Girko, Vʼjačeslav Leonidovyč 1946- |
| author_variant | v l g vl vlg |
| building | Verbundindex |
| bvnumber | BV011280593 |
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| classification_rvk | QH 140 SK 905 SK 915 |
| ctrlnum | (OCoLC)35055550 (DE-599)BVBBV011280593 |
| dewey-full | 519.5/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/3 |
| dewey-search | 519.5/3 |
| dewey-sort | 3519.5 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV011280593 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:07:05Z |
| institution | BVB |
| isbn | 0898640784 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007575952 |
| oclc_num | 35055550 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-384 DE-706 DE-11 |
| owner_facet | DE-12 DE-703 DE-384 DE-706 DE-11 |
| physical | XXIV, 320 S. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Allerton Press |
| record_format | marc |
| spelling | Girko, Vʼjačeslav Leonidovyč 1946- Verfasser (DE-588)1055764976 aut Theory of linear algebraic equations with random coefficients Vyacheslav L. Girko New York Allerton Press 1996 XXIV, 320 S. txt rdacontent n rdamedia nc rdacarrier Lineaire algebra gtt Matrices gtt Multivariate analyse gtt Equations Numerical solutions Random variables Algebraische Gleichung (DE-588)4001162-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Zufallskoeffizient (DE-588)4191647-5 gnd rswk-swf Algebraische Gleichung (DE-588)4001162-8 s Zufallskoeffizient (DE-588)4191647-5 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007575952&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Girko, Vʼjačeslav Leonidovyč 1946- Theory of linear algebraic equations with random coefficients Lineaire algebra gtt Matrices gtt Multivariate analyse gtt Equations Numerical solutions Random variables Algebraische Gleichung (DE-588)4001162-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Zufallskoeffizient (DE-588)4191647-5 gnd |
| subject_GND | (DE-588)4001162-8 (DE-588)4128130-5 (DE-588)4191647-5 |
| title | Theory of linear algebraic equations with random coefficients |
| title_auth | Theory of linear algebraic equations with random coefficients |
| title_exact_search | Theory of linear algebraic equations with random coefficients |
| title_full | Theory of linear algebraic equations with random coefficients Vyacheslav L. Girko |
| title_fullStr | Theory of linear algebraic equations with random coefficients Vyacheslav L. Girko |
| title_full_unstemmed | Theory of linear algebraic equations with random coefficients Vyacheslav L. Girko |
| title_short | Theory of linear algebraic equations with random coefficients |
| title_sort | theory of linear algebraic equations with random coefficients |
| topic | Lineaire algebra gtt Matrices gtt Multivariate analyse gtt Equations Numerical solutions Random variables Algebraische Gleichung (DE-588)4001162-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Zufallskoeffizient (DE-588)4191647-5 gnd |
| topic_facet | Lineaire algebra Matrices Multivariate analyse Equations Numerical solutions Random variables Algebraische Gleichung Numerisches Verfahren Zufallskoeffizient |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007575952&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT girkovʼjaceslavleonidovyc theoryoflinearalgebraicequationswithrandomcoefficients |