Introduction to applied linear algebra with MATLAB:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Lemgo
Heldermann
2008
|
| Series: | Sigma series in applied mathematics
7 |
| Subjects: | |
| Online Access: | Inhaltstext Ausführliche Beschreibung Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 499 - 508 |
| Physical Description: | XIII, 517 S. graph. Darst. |
| ISBN: | 9783885384076 |
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SIGAM SERIES IN APPLIED MATHEMATICS VOLUME 7 RIZWAN BUTT INTRODUCTION TO
APPLIED LINEAR ALGEBRA WITH MATLAB HELDERMANN VERLAG CONTENTS NUMBER
SYSTEMS AND ERRORS 1 1.1 INTRODUCTION 1 1.2 NUMBER REPRESENTATION AND
BASE OF NUMBERS 1 1.2.1 NORMALIZED FLOATING-POINT REPRESENTATION 3 1.2.2
ROUNDING AND CHOPPING 5 1.3 ERROR 6 1.4 SOURCES OF ERRORS 7 1.4.1 HUMAN
ERROR 7 1.4.2 TRUNCATION ERROR 8 1.4.3 ROUND-OFF ERROR 8 1.5 EFFECT OF
ROUND-OFF ERRORS IN ARITHMETIC OPERATION 9 1.5.1 ROUNDING^OFF ERRORS IN
ADDITION AND SUBTRACTION 9 1.5.2 ROUNDING OFF ERRORS IN MULTIPLICATION
10 1.5.3 ROUNDING OFF ERRORS IN DIVISION 12 1.5.4 ROUNDING OFF ERRORS IN
POWERS AND ROOTS .'.- 14 1.6 SUMMARY .'.- .- : ". ?\ 15 1.7 PROBLEMS K
.'. '.I 17 -*,'*?* SYSTEMS OF LINEAR EQUATIONS 19 2.1
INTRODUCTION * * V 19 2.1.1 LINEAR SYSTEM IN MATRIX NOTATION ^ 23 2.2
PROPERTIES OF MATRICES AND DETERMINANT -. 25 2.2.1 INTRODUCTION OF
MATRICES 25 2.2.2 SOME SPECIAL MATRIX FORMS 29 2.2.3 THE DETERMINANT OF
MATRIX 40 2.3 NUMERICAL METHODS FOR LINEAR SYSTEMS 45 2.4 DIRECT METHODS
FOR LINEAR SYSTEMS 46 2.4.1 CRAMER'S RULE 46 . 2.4.2 GAUSSIAN
ELIMINATION METHOD 49 2.4.3 PIVOTING STRATEGIES 61 2.4.4 GAUSS-JORDAN
METHOD 66 2.4.5 LU DECOMPOSITION METHOD 71 2.4.6 TRIDIAGONAL SYSTEMS OF
LINEAR EQUATIONS 90 VIII CONTENTS 2.5 APPLICATIONS 93 2.5.1 CURVE
FITTING, ELECTRIC NETWORKS AND TRAFFIC FLOW 93 2.5.2 HEAT CONDUCTION 100
2.5.3 CHEMICAL SOLUTIONS AND BALANCING CHEMICAL EQUATIONS . 102 2.5.4
MANUFACTURING, SOCIAL, AND FINANCIAL ISSUES 105 2.5.5 ALLOCATION OF
RESOURCES 109 2.6 SUMMARY 110 2.7 PROBLEMS 112 3 CONDITIONING OF LINEAR
SYSTEMS 123 3.1 INTRODUCTION . . 123 3.2 NORMS OF VECTORS AND MATRICES
123 3.3 ERRORS IN SOLVING LINEAR SYSTEMS 127 3.4 SUMMARY 138 3.5
PROBLEMS 139 4 ITERATIVE METHODS FOR LINEAR SYSTEMS 143 4.1 INTRODUCTION
143 4.2 JACOBI ITERATIVE METHOD 144 4.3 GAUSS-SEIDEL ITERATIVE METHOD
149 4.4 CONVERGENCE CRITERIA 153 4.5 EIGENVALUES AND EIGENVECTORS 158
4.6 SUCCESSIVE OVER-RELAXATION METHOD 165 4.7 CONJUGATE GRADIENT METHOD
171 4.8 ITERATIVE REFINEMENT 175 4.9 SUMMARY . .-. .\ 177 4.10
PROBLEMS * .'.'. * 17 8 5 THE EIGENVALUE PROBLEMS 183 5.1
INTRODUCTION . .; 183 5.2 LINEAR ALGEBRA AND EIGENVALUES PROBLEMS . . .
. , 193 5.3 DIAGONALIZATION OF MATRICES . ." ~. 197 5.4 BASIC PROPERTIES
OF EIGENVALUE PROBLEMS 209 5.5 SOME RESULTS OF EIGENVALUES PROBLEMS 224
5.6 APPLICATIONS OF EIGENVALUE PROBLEMS 227 5.6.1 SYSTEM OF DIFFERENTIAL
EQUATIONS 227 5.6.2 DIFFERENCE EQUATIONS 233 5.7 SUMMARY 237 5.8
PROBLEMS 238 6 NUMERICAL COMPUTATION OF EIGENVALUES 243 6.1 INTRODUCTION
243 6.2 VECTOR ITERATIVE METHODS FOR EIGENVALUES 244 6.2.1 POWER METHOD
244 CONTENTS IX 6.2.2 INVERSE POWER METHOD 248 6.2.3 SHIFTED INVERSE
POWER METHOD 251 6.3 LOCATION OF THE EIGENVALUES 255 6.3.1 GERSCHGORIN
CIRCLES THEOREM 255 6.3.2 RAYLEIGH QUOTIENT 256 6.4 INTERMEDIATE
EIGENVALUES 258 6.5 EIGENVALUES OF SYMMETRIC MATRICES 261 6.5.1 JACOBI
METHOD 262 6.5.2 STURM SEQUENCE ITERATION 268 6.5.3 GIVEN'S METHOD 271
6.5.4 HOUSEHOLDER'S METHOD 275 6.6 MATRIX DECOMPOSITION METHODS 279
6.6.1 QR METHOD 279 6.6.2 LR METHOD 283 6.6.3 UPPER HESSENBERG FORM 285
6.6.4 SINGULAR VALUE DECOMPOSITION 292 6.7 SUMMARY 299 6.8 PROBLEMS 300
7 APPROXIMATING FUNCTIONS 307 7.1 INTRODUCTION 307 7.2 POLYNOMIAL
APPROXIMATION * 308 7.2.1 AITKEN'S^METHOD 308 7.3 LEAST SQUARES
APPROXIMATION 312 7.3.1 LINEAR LEAST SQUARES 313 7.3.2 POLYNOMIAL LEAST
SQUARES 317 7.3.3 NONLINEAR LEAST SQUARES *'.'** F. '. '. $\ 321 7.3.4
LEAST SQUARES PLANE . C . V. RI 328 7.3.5 LEAST SQUARES SOLUTION
OF A OVERDETERMINECTSYSTEM . . . . . 330 7.3.6 LEAST SQUARES WITH QR
DECOMPOSITION . . ."/ 334 7.3.7 LEAST SQUARES WITH SINGULAR VALUE
DECOMPOSITION 339 7.4 SUMMARY _ '. S. 344 7.5 PROBLEMS " '. 345 8 LINEAR
PROGRAMMING 351 8.1 INTRODUCTION 351 8.2 GENERAL FORMULATION 352 8.2.1
TERMINOLOGY 353 8.3 LINEAR PROGRAMMING PROBLEMS 353 8.4 GRAPHICAL
SOLUTION OF LP MODELS 356 8.4.1 REVERSED INEQUALITY CONSTRAINTS 362
8.4.2 EQUALITY CONSTRAINTS 362 8.4.3 MINIMUM VALUE OF A FUNCTION 362
8.4.4 LINEAR PROGRAM IN CANONICAL FORM 368 X CONTENTS 8.4.5 LINEAR
PROGRAM IN STANDARD FORM 369 8.4.6 SOME IMPORTANT DEFINITIONS 372 8.5
THE SIMPLEX METHOD 373 8.5.1 UNRESTRICTED-IN-SIGN VARIABLES 381 8.6
FINDING A FEASIBLE BASIS 383 8.6.1 BIG M SIMPLEX METHOD 385 8.6.2
TWO-PHASE SIMPLEX METHOD 387 8.7 DUALITY 391 8.7.1 COMPARISON OF PRIMAL
AND DUAL PROBLEMS 393 8.7.2 PRIMAL-DUAL PROBLEMS IN STANDARD FORM 395
8.8 SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING 400 8.9 SUMMARY 402 8.10
PROBLEMS 403 APPENDICES 413 A COMPLEX NUMBERS AND INNER PRODUCTS 413 A.I
COMPLEX NUMBERS 413 A.I.I GEOMETRIC REPRESENTATION OF COMPLEX NUMBER 414
A. 1.2 OPERATIONS ON COMPLEX NUMBERS 414 A.1.3 POLAR FORM OF COMPLEX
NUMBER 416 A. 1.4 MATRICES WITH COMPLEX ENTRIES 419 A. 1.5 SOLVING
SYSTEMS WITH COMPLEX ENTRIES 420 A.1.6 DETERMINANTS OF COMPLEX NUMBERS
420 A.I.7 COMPLEX EIGENVALUES AND EIGENVECTORS 421 A.2 INNER PRODUCT
SPACE ". 421 A.2.1 PROPERTIES OF INNER PRODUCTS \': :. '. . R 422 A.2.2
COMPLEX INNER PRODUCTS . . R . .".,;. 425 B INTRODUCTION OF
MATLAB 427 B.I MATLAB BUILT-IN-FUNCTIONS ;, 463 B.2 SYMBOLIC
COMPUTATION . Y 465 B.3 SYMBOLIC MATH TOOLBOX FUNCTIONS '. 481 B.4
INDEX OF MATLAB PROGRAMS 482 C ANSWERS TO SELECTED PROBLEMS 485
BIBLIOGRAPHY 508 INDEX 509 |
| adam_txt |
SIGAM SERIES IN APPLIED MATHEMATICS VOLUME 7 RIZWAN BUTT INTRODUCTION TO
APPLIED LINEAR ALGEBRA WITH MATLAB HELDERMANN VERLAG CONTENTS NUMBER
SYSTEMS AND ERRORS 1 1.1 INTRODUCTION 1 1.2 NUMBER REPRESENTATION AND
BASE OF NUMBERS 1 1.2.1 NORMALIZED FLOATING-POINT REPRESENTATION 3 1.2.2
ROUNDING AND CHOPPING 5 1.3 ERROR 6 1.4 SOURCES OF ERRORS 7 1.4.1 HUMAN
ERROR 7 1.4.2 TRUNCATION ERROR 8 1.4.3 ROUND-OFF ERROR 8 1.5 EFFECT OF
ROUND-OFF ERRORS IN ARITHMETIC OPERATION 9 1.5.1 ROUNDING^OFF ERRORS IN
ADDITION AND SUBTRACTION 9 1.5.2 ROUNDING OFF ERRORS IN MULTIPLICATION
10 1.5.3 ROUNDING OFF ERRORS IN DIVISION 12 1.5.4 ROUNDING OFF ERRORS IN
POWERS AND ROOTS .'.- 14 1.6 SUMMARY .'.- .- : ". ?\ 15 1.7 PROBLEMS K
.'. '.I 17 -*,'*?* SYSTEMS OF LINEAR EQUATIONS 19 2.1
INTRODUCTION * * V 19 2.1.1 LINEAR SYSTEM IN MATRIX NOTATION ^ 23 2.2
PROPERTIES OF MATRICES AND DETERMINANT -. 25 2.2.1 INTRODUCTION OF
MATRICES 25 2.2.2 SOME SPECIAL MATRIX FORMS 29 2.2.3 THE DETERMINANT OF
MATRIX 40 2.3 NUMERICAL METHODS FOR LINEAR SYSTEMS 45 2.4 DIRECT METHODS
FOR LINEAR SYSTEMS 46 2.4.1 CRAMER'S RULE 46 . 2.4.2 GAUSSIAN
ELIMINATION METHOD 49 2.4.3 PIVOTING STRATEGIES 61 2.4.4 GAUSS-JORDAN
METHOD 66 2.4.5 LU DECOMPOSITION METHOD 71 2.4.6 TRIDIAGONAL SYSTEMS OF
LINEAR EQUATIONS 90 VIII CONTENTS 2.5 APPLICATIONS 93 2.5.1 CURVE
FITTING, ELECTRIC NETWORKS AND TRAFFIC FLOW 93 2.5.2 HEAT CONDUCTION 100
2.5.3 CHEMICAL SOLUTIONS AND BALANCING CHEMICAL EQUATIONS . 102 2.5.4
MANUFACTURING, SOCIAL, AND FINANCIAL ISSUES 105 2.5.5 ALLOCATION OF
RESOURCES 109 2.6 SUMMARY 110 2.7 PROBLEMS 112 3 CONDITIONING OF LINEAR
SYSTEMS 123 3.1 INTRODUCTION . . 123 3.2 NORMS OF VECTORS AND MATRICES
123 3.3 ERRORS IN SOLVING LINEAR SYSTEMS 127 3.4 SUMMARY 138 3.5
PROBLEMS 139 4 ITERATIVE METHODS FOR LINEAR SYSTEMS 143 4.1 INTRODUCTION
143 4.2 JACOBI ITERATIVE METHOD 144 4.3 GAUSS-SEIDEL ITERATIVE METHOD
149 4.4 CONVERGENCE CRITERIA 153 4.5 EIGENVALUES AND EIGENVECTORS 158
4.6 SUCCESSIVE OVER-RELAXATION METHOD 165 4.7 CONJUGATE GRADIENT METHOD
171 4.8 ITERATIVE REFINEMENT 175 4.9 SUMMARY . .-. .\ 177 4.10
PROBLEMS * .'.'. * 17 8 5 THE EIGENVALUE PROBLEMS 183 5.1
INTRODUCTION . .; 183 5.2 LINEAR ALGEBRA AND EIGENVALUES PROBLEMS . . .
. , 193 5.3 DIAGONALIZATION OF MATRICES . ." ~. 197 5.4 BASIC PROPERTIES
OF EIGENVALUE PROBLEMS 209 5.5 SOME RESULTS OF EIGENVALUES PROBLEMS 224
5.6 APPLICATIONS OF EIGENVALUE PROBLEMS 227 5.6.1 SYSTEM OF DIFFERENTIAL
EQUATIONS 227 5.6.2 DIFFERENCE EQUATIONS 233 5.7 SUMMARY 237 5.8
PROBLEMS 238 6 NUMERICAL COMPUTATION OF EIGENVALUES 243 6.1 INTRODUCTION
243 6.2 VECTOR ITERATIVE METHODS FOR EIGENVALUES 244 6.2.1 POWER METHOD
244 CONTENTS IX 6.2.2 INVERSE POWER METHOD 248 6.2.3 SHIFTED INVERSE
POWER METHOD 251 6.3 LOCATION OF THE EIGENVALUES 255 6.3.1 GERSCHGORIN
CIRCLES THEOREM 255 6.3.2 RAYLEIGH QUOTIENT 256 6.4 INTERMEDIATE
EIGENVALUES 258 6.5 EIGENVALUES OF SYMMETRIC MATRICES 261 6.5.1 JACOBI
METHOD 262 6.5.2 STURM SEQUENCE ITERATION 268 6.5.3 GIVEN'S METHOD 271
6.5.4 HOUSEHOLDER'S METHOD 275 6.6 MATRIX DECOMPOSITION METHODS 279
6.6.1 QR METHOD 279 6.6.2 LR METHOD 283 6.6.3 UPPER HESSENBERG FORM 285
6.6.4 SINGULAR VALUE DECOMPOSITION 292 6.7 SUMMARY 299 6.8 PROBLEMS 300
7 APPROXIMATING FUNCTIONS 307 7.1 INTRODUCTION 307 7.2 POLYNOMIAL
APPROXIMATION * 308 7.2.1 AITKEN'S^METHOD 308 7.3 LEAST SQUARES
APPROXIMATION 312 7.3.1 LINEAR LEAST SQUARES 313 7.3.2 POLYNOMIAL LEAST
SQUARES 317 7.3.3 NONLINEAR LEAST SQUARES *'.'** F. '. '. $\ 321 7.3.4
LEAST SQUARES PLANE . C . V. RI 328 7.3.5 LEAST SQUARES SOLUTION
OF A OVERDETERMINECTSYSTEM . . . . . 330 7.3.6 LEAST SQUARES WITH QR
DECOMPOSITION . . ."/ 334 7.3.7 LEAST SQUARES WITH SINGULAR VALUE
DECOMPOSITION 339 7.4 SUMMARY _ '. S. 344 7.5 PROBLEMS " '. 345 8 LINEAR
PROGRAMMING 351 8.1 INTRODUCTION 351 8.2 GENERAL FORMULATION 352 8.2.1
TERMINOLOGY 353 8.3 LINEAR PROGRAMMING PROBLEMS 353 8.4 GRAPHICAL
SOLUTION OF LP MODELS 356 8.4.1 REVERSED INEQUALITY CONSTRAINTS 362
8.4.2 EQUALITY CONSTRAINTS 362 8.4.3 MINIMUM VALUE OF A FUNCTION 362
8.4.4 LINEAR PROGRAM IN CANONICAL FORM 368 X CONTENTS 8.4.5 LINEAR
PROGRAM IN STANDARD FORM 369 8.4.6 SOME IMPORTANT DEFINITIONS 372 8.5
THE SIMPLEX METHOD 373 8.5.1 UNRESTRICTED-IN-SIGN VARIABLES 381 8.6
FINDING A FEASIBLE BASIS 383 8.6.1 BIG M SIMPLEX METHOD 385 8.6.2
TWO-PHASE SIMPLEX METHOD 387 8.7 DUALITY 391 8.7.1 COMPARISON OF PRIMAL
AND DUAL PROBLEMS 393 8.7.2 PRIMAL-DUAL PROBLEMS IN STANDARD FORM 395
8.8 SENSITIVITY ANALYSIS IN LINEAR PROGRAMMING 400 8.9 SUMMARY 402 8.10
PROBLEMS 403 APPENDICES 413 A COMPLEX NUMBERS AND INNER PRODUCTS 413 A.I
COMPLEX NUMBERS 413 A.I.I GEOMETRIC REPRESENTATION OF COMPLEX NUMBER 414
A. 1.2 OPERATIONS ON COMPLEX NUMBERS 414 A.1.3 POLAR FORM OF COMPLEX
NUMBER 416 A. 1.4 MATRICES WITH COMPLEX ENTRIES 419 A. 1.5 SOLVING
SYSTEMS WITH COMPLEX ENTRIES 420 A.1.6 DETERMINANTS OF COMPLEX NUMBERS
420 A.I.7 COMPLEX EIGENVALUES AND EIGENVECTORS 421 A.2 INNER PRODUCT
SPACE ". 421 A.2.1 PROPERTIES OF INNER PRODUCTS \': :. '. . R 422 A.2.2
COMPLEX INNER PRODUCTS . . R . .".,;. 425 B INTRODUCTION OF
MATLAB 427 B.I MATLAB BUILT-IN-FUNCTIONS ;, 463 B.2 SYMBOLIC
COMPUTATION . Y 465 B.3 SYMBOLIC MATH TOOLBOX FUNCTIONS '. 481 B.4
INDEX OF MATLAB PROGRAMS 482 C ANSWERS TO SELECTED PROBLEMS 485
BIBLIOGRAPHY 508 INDEX 509 |
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| callnumber-label | QA185 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 220 |
| ctrlnum | (OCoLC)239670195 (DE-599)DNB988793016 |
| dewey-full | 512.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.9 |
| dewey-search | 512.9 |
| dewey-sort | 3512.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| index_date | 2024-07-02T21:18:44Z |
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| isbn | 9783885384076 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016570828 |
| oclc_num | 239670195 |
| open_access_boolean | |
| owner | DE-29T DE-703 DE-634 DE-92 |
| owner_facet | DE-29T DE-703 DE-634 DE-92 |
| physical | XIII, 517 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Heldermann |
| record_format | marc |
| series | Sigma series in applied mathematics |
| series2 | Sigma series in applied mathematics |
| spelling | Butt, Rizwan Verfasser aut Introduction to applied linear algebra with MATLAB Rizwan Butt Lemgo Heldermann 2008 XIII, 517 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Sigma series in applied mathematics 7 Literaturverz. S. 499 - 508 MATLAB Datenverarbeitung Algebras, Linear Data processing Lineare Algebra (DE-588)4035811-2 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 s MATLAB (DE-588)4329066-8 s DE-604 Sigma series in applied mathematics 7 (DE-604)BV001902107 7 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3111178&prov=M&dok_var=1&dok_ext=htm Inhaltstext text/html http://www.heldermann.de/SSAM/SSAM07/ssam07.htm Ausführliche Beschreibung HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016570828&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Butt, Rizwan Introduction to applied linear algebra with MATLAB Sigma series in applied mathematics MATLAB Datenverarbeitung Algebras, Linear Data processing Lineare Algebra (DE-588)4035811-2 gnd MATLAB (DE-588)4329066-8 gnd |
| subject_GND | (DE-588)4035811-2 (DE-588)4329066-8 |
| title | Introduction to applied linear algebra with MATLAB |
| title_auth | Introduction to applied linear algebra with MATLAB |
| title_exact_search | Introduction to applied linear algebra with MATLAB |
| title_exact_search_txtP | Introduction to applied linear algebra with MATLAB |
| title_full | Introduction to applied linear algebra with MATLAB Rizwan Butt |
| title_fullStr | Introduction to applied linear algebra with MATLAB Rizwan Butt |
| title_full_unstemmed | Introduction to applied linear algebra with MATLAB Rizwan Butt |
| title_short | Introduction to applied linear algebra with MATLAB |
| title_sort | introduction to applied linear algebra with matlab |
| topic | MATLAB Datenverarbeitung Algebras, Linear Data processing Lineare Algebra (DE-588)4035811-2 gnd MATLAB (DE-588)4329066-8 gnd |
| topic_facet | MATLAB Datenverarbeitung Algebras, Linear Data processing Lineare Algebra |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=3111178&prov=M&dok_var=1&dok_ext=htm http://www.heldermann.de/SSAM/SSAM07/ssam07.htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016570828&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001902107 |
| work_keys_str_mv | AT buttrizwan introductiontoappliedlinearalgebrawithmatlab |