Numerical linear algebra:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Philadelphia
SIAM
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XII, 361 S. graph. Darst. |
| ISBN: | 0898713617 9780898713619 |
Staff View
MARC
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| 100 | 1 | |a Trefethen, Lloyd N. |d 1955- |e Verfasser |0 (DE-588)135818818 |4 aut | |
| 245 | 1 | 0 | |a Numerical linear algebra |c Lloyd N. Trefethen ; David Bau |
| 264 | 1 | |a Philadelphia |b SIAM |c 1997 | |
| 300 | |a XII, 361 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Numerična analiza - Numerična linearna algebra | |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
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Record in the Search Index
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/SK 915 T786 |
| DE-BY-FWS_katkey | 559488 |
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| _version_ | 1824553982372085760 |
| 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.
|
| any_adam_object | 1 |
| author | Trefethen, Lloyd N. 1955- Bau, David |
| author_GND | (DE-588)135818818 (DE-588)135818907 |
| author_facet | Trefethen, Lloyd N. 1955- Bau, David |
| author_role | aut aut |
| author_sort | Trefethen, Lloyd N. 1955- |
| author_variant | l n t ln lnt d b db |
| building | Verbundindex |
| bvnumber | BV011346032 |
| classification_rvk | SK 915 QH 140 SK 220 |
| classification_tum | MAT 657f |
| ctrlnum | (OCoLC)440060951 (DE-599)BVBBV011346032 |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2025-02-20T06:44:31Z |
| institution | BVB |
| isbn | 0898713617 9780898713619 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007623776 |
| oclc_num | 440060951 |
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| physical | XII, 361 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | SIAM |
| record_format | marc |
| 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 |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 915 T786 |
|---|---|
| Copy 1 | ausleihbar Checked out – Due: 30.10.2025 Recall This |