Verfügbarkeit: Numerical linear algebra

Numerical linear algebra:

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Bibliographische Detailangaben
Hauptverfasser:	Trefethen, Lloyd N. 1955- (VerfasserIn), Bau, David (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Philadelphia SIAM 1997
Schlagworte:	Numerična analiza - Numerična linearna algebra Numerisches Verfahren Lineare Algebra Numerische Mathematik
Online-Zugang:	Inhaltsverzeichnis Klappentext
Beschreibung:	Hier auch später erschienene, unveränderte Nachdrucke
Beschreibung:	XII, 361 S. graph. Darst.
ISBN:	0898713617 9780898713619

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MARC


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Datensatz im Suchindex

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adam_text	Contents Preface ix Acknowledgments xi I Fundamentals 1 Lecture 1 Matrix-Vector Multiplication .............. 3 Lecture 2 Orthogonal Vectors and Matrices ............ 11 Lecture 3 Norms .......................... 17 Lecture 4 The Singular Value Decomposition ........... 25 Lecture 5 More on the SVD .................... 32 II QR Factorization and Least Squares 39 Lecture б Projectors ........................ 41 Lecture 7 QR Factorization .................... 48 Lecture 8 Gram-Schmidt Orthogonalization ........... 56 Lecture 9 MATLAB ........................ 63 Lecture 10 Householder Triangularization ............. 69 Lecture 11 Least Squares Problems ................. 77 III Conditioning and Stability 87 Lecture 12 Conditioning and Condition Numbers ......... 89 Lecture 13 Floating Point Arithmetic ................ 97 Lecture 14 Stability ......................... 102 Lecture 15 More on Stability .................... 108 Lecture 16 Stability of Householder Triangularization ....... 114 Lecture 17 Stability of Back Substitution ............. 121 Lecture 18 Conditioning of Least Squares Problems ........ 129 Lecture 19 Stability of Least Squares Algorithms ......... 137 Vlil Contents IV Systems of Equations 145 Lecture 20 Gaussian Elimination .................. 147 Lecture 21 Pivoting ......................... 155 Lecture 22 Stability of Gaussian Elimination ........... 163 Lecture 23 Cholesky Factorization ................. 172 V Eigenvalues 179 Lecture 24 Eigenvalue Problems .................. 181 Lecture 25 Overview of Eigenvalue Algorithms .......... 190 Lecture 26 Reduction to Hessenberg or Tridiagonal Form ..... 196 Lecture 27 Rayleigh Quotient, Inverse Iteration .......... 202 Lecture 28 QR Algorithm without Shifts .............. 211 Lecture 29 QR Algorithm with Shifts ................ 219 Lecture 30 Other Eigenvalue Algorithms .............. 225 Lecture 31 Computing the SVD ................... 234 VI Iterative Methods 241 Lecture 32 Overview of Iterative Methods ............. 243 Lecture 33 The Arnoldi Iteration .................. 250 Lecture 34 How Arnoldi Locates Eigenvalues ........... 257 Lecture 35 GMRES ......................... 266 Lecture 36 The Lanczos Iteration .................. 276 Lecture 37 From Lanczos to Gauss Quadrature .......... 285 Lecture 38 Conjugate Gradients .................. 293 Lecture 39 Biorthogonalization Methods .............. 303 Lecture 40 Preconditioning ..................... 313 Appendix The Definition of Numerical Analysis 321 Notes Bibliography Index 329 343 353 A beautifully written textbook offering a distinctive and original treatment. It will be of use to all who teach or study the subject. — Nicholas J. Higham, Professor of Applied Mathematics, University of Manchester. Numerical Linear Algebra is a concise, insightful, and elegant introduction to the field of numerical linear algebra. Professors looking for an elegant presentation of the topic will find it an excellent teaching tool for a one-semester graduate or advanced undergraduate course. The authors1 clear, inviting style and evident love of the field, along with their eloquent presentation of the most fundamental ideas in numerical linear algebra, make it popular with teachers and students alike. A major contribution to the applied mathematics literature, most researchers in the field will consider Numerical Linear Algebra a necessary addition to their personal collections.
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isbn	0898713617 9780898713619
language	English
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spellingShingle	Trefethen, Lloyd N. 1955- Bau, David Numerical linear algebra Numerična analiza - Numerična linearna algebra Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Algebra (DE-588)4035811-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd
subject_GND	(DE-588)4128130-5 (DE-588)4035811-2 (DE-588)4042805-9
title	Numerical linear algebra
title_auth	Numerical linear algebra
title_exact_search	Numerical linear algebra
title_full	Numerical linear algebra Lloyd N. Trefethen ; David Bau
title_fullStr	Numerical linear algebra Lloyd N. Trefethen ; David Bau
title_full_unstemmed	Numerical linear algebra Lloyd N. Trefethen ; David Bau
title_short	Numerical linear algebra
title_sort	numerical linear algebra
topic	Numerična analiza - Numerična linearna algebra Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Algebra (DE-588)4035811-2 gnd Numerische Mathematik (DE-588)4042805-9 gnd
topic_facet	Numerična analiza - Numerična linearna algebra Numerisches Verfahren Lineare Algebra Numerische Mathematik
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007623776&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007623776&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT trefethenlloydn numericallinearalgebra AT baudavid numericallinearalgebra

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