Numerical linear algebra:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Philadelphia, PA
SIAM, Society for Industrial and Applied Mathematics
[2022]
|
| Ausgabe: | Twenty-fifth anniversary edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvi, 370 Seiten Diagramme |
| ISBN: | 9781611977158 |
Internformat
MARC
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Datensatz im Suchindex
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Contents ix Foreword xiii Preface Acknowledgments xv Fundamentals I Lecture Lecture Lecture Lecture Lecture II 1 2 3 4 5 1 Matrix-Vector Multiplication. Orthogonal Vectors and Matrices. Norms . The Singular Value Decomposition. More on the SVD. QR Factorization andLeast Squares Lecture Lecture Lecture Lecture Lecture Lecture III 6 7 8 9 10 11 Projectors. QR Factorization . Gram-Schmidt Orthogonalization. MATLAB . Householder Triangularization. Least Squares Problems. Conditioning andStability Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture 12 13 14 15 16 17 18 19 Conditioning and Condition Numbers. Floating Point Arithmetic. Stability. More on Stability. Stability of Householder Triangularization. Stability of Back Substitution . Conditioning of Least Squares
Problems. Stability of Least Squares Algorithms. vii 3 11 17 25 32 39 41 48 56 63 69 77 87 89 97 102 108 114 121 129 137
viii Contents IV Systems of Equations Lecture Lecture Lecture Lecture V 20 21 22 23 Gaussian Elimination. Pivoting. Stability of Gaussian Elimination . Cholesky Factorization. Eigenvalues Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 147 155 163 172 179 Eigenvalue Problems . 181 Overview of Eigenvalue Algorithms. 190 Reduction to Hessenberg or Tridiagonal Form. 196 Rayleigh Quotient, Inverse Iteration. 202 QR Algorithm without Shifts. 211 QR Algorithm with Shifts. 219 Other Eigenvalue Algorithms. 225 Computing the SVD. 234 VI Iterative Methods Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture 145 241 Overview of Iterative Methods. 243 The Arnoldi Iteration. 250 How Arnoldi Locates Eigenvalues . 257 GMRES . 266 The Lanczos Iteration. 276 From Lanczos to Gauss
Quadrature. 285 Conjugate Gradients . 293 Biorthogonalization Methods. 303 Preconditioning. 313 Appendix TheDefinition of Numerical Analysis 321 Notes 329 Bibliography 343 Index 353 Afterword: Major Developments in Numerical Linear Algebra Since 1997 363 |
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| dewey-full | 512.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.5 |
| dewey-search | 512.5 |
| dewey-sort | 3512.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Twenty-fifth anniversary edition |
| format | Book |
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| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:57:46Z |
| indexdate | 2024-07-10T09:41:16Z |
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| isbn | 9781611977158 |
| language | English |
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| physical | xvi, 370 Seiten Diagramme |
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| publisher | SIAM, Society for Industrial and Applied Mathematics |
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| spelling | Trefethen, Lloyd N. 1955- Verfasser (DE-588)135818818 aut Numerical linear algebra Lloyd N. Trefethen (Oxford University, Oxford, United Kingdom), David Bau (Microsoft Corporation, Redmond, Washington) Twenty-fifth anniversary edition Philadelphia, PA SIAM, Society for Industrial and Applied Mathematics [2022] © 2022 xvi, 370 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Lineare Algebra (DE-588)4035811-2 gnd rswk-swf Algebras, Linear Numerical calculations Lineare Algebra (DE-588)4035811-2 s DE-604 Numerisches Verfahren (DE-588)4128130-5 s Numerische Mathematik (DE-588)4042805-9 s Bau, David Verfasser (DE-588)135818907 aut Erscheint auch als Online-Ausgabe 978-1-611977-16-5 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033928966&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Trefethen, Lloyd N. 1955- Bau, David Numerical linear algebra Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4128130-5 (DE-588)4035811-2 |
| title | Numerical linear algebra |
| title_auth | Numerical linear algebra |
| title_exact_search | Numerical linear algebra |
| title_exact_search_txtP | Numerical linear algebra |
| title_full | Numerical linear algebra Lloyd N. Trefethen (Oxford University, Oxford, United Kingdom), David Bau (Microsoft Corporation, Redmond, Washington) |
| title_fullStr | Numerical linear algebra Lloyd N. Trefethen (Oxford University, Oxford, United Kingdom), David Bau (Microsoft Corporation, Redmond, Washington) |
| title_full_unstemmed | Numerical linear algebra Lloyd N. Trefethen (Oxford University, Oxford, United Kingdom), David Bau (Microsoft Corporation, Redmond, Washington) |
| title_short | Numerical linear algebra |
| title_sort | numerical linear algebra |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Numerische Mathematik Numerisches Verfahren Lineare Algebra |
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