Numerical linear algebra with applications: using matlab
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| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Amsterdam [u.a.]
Elsevier
2015
|
| Ausgabe: | 1. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XXVI, 602 S. Ill., graph. Darst. |
| ISBN: | 012394435X 9780123944351 |
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MARC
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| 020 | |a 9780123944351 |9 978-0-12-394435-1 | ||
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| 100 | 1 | |a Ford, William |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Numerical linear algebra with applications |b using matlab |c by William Ford |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a Amsterdam [u.a.] |b Elsevier |c 2015 | |
| 300 | |a XXVI, 602 S. |c Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a MATLAB |0 (DE-588)4329066-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Online-Ressource |0 (DE-588)4511937-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Lineare Algebra |0 (DE-588)4035811-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Lineare Algebra |0 (DE-588)4035811-2 |D s |
| 689 | 0 | 1 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
| 689 | 0 | 2 | |a MATLAB |0 (DE-588)4329066-8 |D s |
| 689 | 0 | 3 | |a Online-Ressource |0 (DE-588)4511937-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026923148&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Passau - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026923148&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-026923148 | ||
Datensatz im Suchindex
| DE-BY-862_location | 2000 |
|---|---|
| DE-BY-FWS_call_number | 2000/ST 601 M35 F711 |
| DE-BY-FWS_katkey | 559490 |
| DE-BY-FWS_media_number | 083000515038 |
| _version_ | 1824553982362648577 |
| adam_text | Contents
List of
Figures
XIII
4.
Determinants
59
List of Algorithms
xvii
Preface
xix
4.1.
Developing the Determinant of a
2
χ
2
and a
3
χ
3
Matrix
59
4.2.
Expansion by Minors
60
1.
Matrices
1
4.3.
Computing a Determinant Using Row
1.1.
Matrix Arithmetic
1
Operations
64
1.1.1.
Matrix Product
2
4.4.
Application: Encryption
71
1.1.2.
The Trace
5
4.5.
Chapter Summary
73
1.1.3.
MATLAB
Examples
6
4.6.
Problems
74
1.2.
Linear Transformations
7
4.6.1.
MATLAB
Problems
76
1.2.1.
Rotations
7
1.3.
Powers of Matrices
11
1.4.
Nonsingular Matrices
13
5.
Eigenvalues and Eigenvectors
79
1.5.
The Matrix Transpose and Symmetric
5.1.
Definitions and Examples
79
Matrices
16
5.2.
Selected Properties of Eigenvalues
1.6.
Chapter Summary
18
and Eigenvectors
83
1.7.
Problems
19
5.3.
Diagonalization
84
1.7.1.
MATLAB
Problems
22
5,3,1,
Powers of Matrices
88
2.
Linear Equations
25
5.4.
Applications
5.4.1.
Electric Circuit
89
89
2.1.
Introduction to Linear Equations
25
5.4.2.
Irreducible Matrices
91
2.2.
Solving Square Linear Systems
27
5.4.3.
Ranking of Teams Using
2.3.
Gaussian Elimination
28
Eigenvectors
94
2.3.1.
Upper-Triangular Form
29
5.5.
Computing Eigenvalues and Eigenvectors
2.4.
Systematic Solution of Linear Systems
31
using
MATLAB
95
2.5.
Computing the Inverse
34
5.6.
Chapter Summary
96
2.6.
Homogeneous Systems
36
5.7.
Problems
97
2.7.
Application: A Truss
37
5.7.1.
MATLAB
Problems
99
2.8.
Application: Electrical Circuit
39
2.9.
Chapter Summary
40
2.10.
Problems
42
6.
Orthogonal Vectors
2.10.1.
MATLAB
Problems
43
and Matrices
103
3.
Subspaces
47
6.1.
Introduction
103
6.2.
The Inner Product
104
3.1.
Introduction
47
6.3.
Orthogonal Matrices
107
3.2.
Subspaces of
Ά
47
6.4.
Symmetric Matrices and Orthogonality
109
3.3.
Linear Independence
49
6.5.
The L2 Inner Product
110
3.4.
Basis of a Subspace
50
6.6.
The Cauchy-Schwarz Inequality
111
3.5.
The Rank of a Matrix
51
6.7.
Signal Comparison
112
3.6.
Chapter Summary
55
6.8.
Chapter Summary
113
3.7.
Problems
56
6.9.
Problems
114
3.7.1.
MATLAB
Problems
57
f, Q
1
λ
/ІДТІ
AR PmUomc
1 1
A
7.
Vector and Matrix
Norms
119
7.1.
Vector Norms
7.1.1.
Properties of the
2
-Norm
7.1.2.
Spherical Coordinates
7.2.
Matrix Norms
7.2.1.
The Frobenius Matrix Norm
7.2.2.
Induced Matrix Norms
7.3.
Submultiplicative
Matrix Norms
7.4.
Computing the Matrix 2-Norm
7.5.
Properties of the Matrix 2-Norm
7.6.
Chapter Summary
7.7.
Problems
7.7.1.
MATLAB
Problems
8.
Floating Point Arithmetic
8.1.
Integer Representation
8.2. Floating-Point
Representation
8.2.1.
Mapping from Real Numbers
to
Floating-Point
Numbers
8.3. Floating-Point
Arithmetic
8.3.1.
Relative Error
8.3.2.
Rounding Error Bounds
8.4.
Minimizing Errors
8.4.1.
Avoid Adding a Huge Number to a
Small Number
155
8.4.2.
Avoid Subtracting Numbers That Are
Close
155
8.5.
Chapter Summary
156
8.6.
Problems
158
8.6.1.
MATLAB
Problems
160
9.
Algorithms
163
9.1.
Pseudocode Examples
163
9.1.1.
Inner Product of Two Vectors
164
9.1.2.
Computing the Frobenius
Norm
164
9.1.3.
Matrix Multiplication
164
9.1.4.
Block Matrices
165
9.2.
Algorithm Efficiency
166
9.2.1.
Smaller Flop Count Is Not
Always Better
168
9.2.2.
Measuring Truncation Error
168
9.3.
The Solution to Upper and Lower
Triangular Systems
168
9.3.1.
Efficiency Analysis
170
9.4.
The Thomas Algorithm
171
9.4.1.
Efficiency Analysis
173
9.5.
Chapter Summary
174
9.6.
Problems
175
9.6.1.
MATLAB
Problems
177
10.
Conditioning of Problems
and Stability of Algorithms
119
.ч.
■ ■
v-
121
10.1.
123
126
10.2.
127
127
131
10.3.
132
136
138
10.4.
140
10.5.
142
1
Ą
p
10.6.
1
45
145
10.7.
147
10.8.
148
10.9.
150
150
151
10.10
10.11
155
181
Why Do We Need Numerical
Linear Algebra?
181
Computation Error
183
10.2.1.
Forward Error
183
10.2.2.
Backward Error
184
Algorithm Stability
185
10.3.1.
Examples of Unstable
Algorithms
186
Conditioning of a Problem
187
Perturbation Analysis for Solving a
Linear System
190
Properties of the Matrix Condition
Number
193
MATLAB
Computation of a Matrix
Condition Number
195
Estimating the Condition Number
195
Introduction to Perturbation Analysis
of Eigenvalue Problems
196
Chapter Summary
197
Problems
199
10.11.1.
MATLAB
Problems
200
11.
Gaussian Elimination and the
Ш
Decomposition
205
11.1.
LU
Decomposition
205
11.2.
Using
LU
to Solve Equations
206
11.3.
Elementary Row Matrices
208
11.4.
Derivation of the
LU
Decomposition
210
11.4.1.
Colon Notation
214
11.4.2.
The
LU
Decomposition
Algorithm
216
11.4.3.
LU
Decomposition Flop
Count
217
11.5.
Gaussian Elimination with Partial
Pivoting
218
11.5.1.
Derivation of
РД=Ш
219
11.5.2.
Algorithm for Gaussian
Elimination with Partial
Pivoting
223
11.6.
Using the
LU
Decomposition to Solve
Ax¡
=
bj,
1 <
і
<
к
225
11.7.
Finding
Л 7
226
11.8.
Stability and Efficiency of Gaussian
Elimination
227
11.9.
Iterative Refinement
228
11.10.
Chapter Summary
230
11.11.
Problems
232
11.11.1.
MATLAB
Problems
236
12. Linear
System
Applications
241
12.1.
Fourier Series
241
12.1.1.
The Square Wave
243
12.2.
Finite Difference Approximations
244
12.2.1.
Steady-State Heat and Diffusion
245
12.3.
Least-Squares Polynomial Fitting
247
12.3.1.
Normal Equations
249
12.4.
Cubic Spline Interpolation
252
12.5.
Chapter Summary
256
12.6.
Problems
257
12.6.1.
MATLAB
Problems
260
13.
Important Special Systems
263
13.1.
Tridiagonal Systems
263
13.2.
Symmetric Positive Definite Matrices
267
13.2.1.
Applications
269
13.3.
The Cholesky Decomposition
269
13.3.1.
Computing the Cholesky
Decomposition
270
13.3.2.
Efficiency
272
13.3.3.
Solving Ax
=
Ъ
If A Is Positive
Definite
272
13.3.4.
Stability
273
13.4.
Chapter Summary
273
13.5.
Problems
274
13.5.1.
MATLAB
Problems
277
14.
Cram-Schmidt Orthonormalization
281
14.1.
The Gram-Schmidt Process
14.2.
Numerical Stability of the
Gram-Schmidt Process
14.3.
The QR Decomposition
14.3.1.
Efficiency
14.3.2.
Stability
14.4.
Applications of the QR Decomposition
14.4.1.
Computing the Determinant
14.4.2.
Finding an
Orthonormal
Basis for
the Range of a Matrix
14.5.
Chapter Summary
14.6.
Problems
14.6.1.
MATLAB
Problems
15.
The Singular Value Decomposition
15.1.
The
SVD
Theorem
15.2.
Using the
SVD
to Determine
Properties of a Matrix
15.2.1.
The Four Fundamental
Subspaces of a Matrix
15.3.
SVD
and Matrix Norms
15.4.
Geometric Interpretation of the
SVD
15.5.
Computing the
SVD
Using
MATLAB
281
284
287
289
290
290
291
291
292
292
293
299
299
302
304
306
307
308
15.6.
Computing
Л
r
309
15.7.
Image Compression Using the
SVD
310
15.7.1.
Image Compression Using
MATLAB
311
15.7.2.
Additional Uses
313
15.8.
Final Comments
314
15.9.
Chapter Summary
314
15.10.
Problems
316
15.10.1.
MATLAB
Problems
317
16.
Least-Squares Problems
321
16.1.
Existence and Uniqueness of
Least-Squares Solutions
322
16.1.1.
Existence and Uniqueness
Theorem
322
16.1.2.
Normal Equations and
Least-Squares Solutions
324
16.1.3.
The
Pseudoinverse, m
>n
324
16.1.4.
The
Pseudoinverse, m<n
325
16.2.
Solving Overdetermined Least-Squares
Problems
325
16.2.1.
Using the Normal Equations
326
16.2.2.
Using the QR Decomposition
327
16.2.3.
Using the
SVD
329
16.2.4.
Remark on Curve Fitting
332
16.3.
Conditioning of Least-Squares
Problems
332
16.3.1.
Sensitivity when using the
Normal Equations
333
16.4.
Rank-Deficient Least-Squares Problems
333
16.4.1.
Efficiency
338
16.5.
Underdetermined Linear Systems
338
16.5.1.
Efficiency
341
16.6.
Chapter Summary
341
16.7.
Problems
342
16.7.1,
MATLAB
Problems
343
17.
Implementing the QR
Decomposition
351
17.1.
Review of the QR Decomposition
Using Gram-Schmidt
351
17.2.
Givens
Rotations
352
17.2.1,
Zeroing a Particular Entry in a
Vector
353
17.3.
Creating a Sequence of Zeros in a
Vector Using
Givens
Rotations
355
17.4.
Product of
a Givens
Matrix with a
General Matrix
356
17.5.
Zeroing-Out Column Entries in a
Matrix Using
Givens
Rotations
357
17.6.
Accurate Computation of the
Givens
Parameters
358
17.7.
The Givens
Algorithm for the QR
Decomposition
359
17.7.1.
The Reduced QR
Decomposition
361
17.7.2.
Efficiency
362
17.8.
Householder Reflections
362
17.8.1.
Matrix Column Zeroing Using
Householder Reflections
365
17,8.2.
Implicit Computation with
Householder Reflections
367
17.9.
Computing the QR Decomposition
Using Householder Reflections
368
17.9.1.
Efficiency and Stability
372
17.10.
Chapter Summary
373
17.11.
Problems
373
17.11.1.
MATLAB
Problems
376
18.
The Algebraic Eigenvalue Problem
379
18.1.
Applications of the Eigenvalue
Problem
379
18.1.1.
Vibrations and Resonance
380
18.1.2.
The Leslie Model in
Population Ecology
383
18.1.3.
Buckling of a Column
386
18.2.
Computation of Selected Eigenvalues
and Eigenvectors
388
18.2.1.
Additional Property of a
Diagonalizable Matrix
389
18.2.2.
The Power Method for
Computing the Dominant
Eigenvalue
390
18.2.3.
Computing the Smallest
Eigenvalue and Corresponding
Eigenvector
393
18.3.
The Basic QR Iteration
394
18.4.
Transformation to Upper
Hessenberg
Form
395
18.4.1.
Efficiency and Stability
400
18.5.
The Unshifted
Hessenberg QR
Iteration
400
18.5.1.
Efficiency
403
18.6.
The Shifted
Hessenberg
QR Iteration
403
18.6.1.
A Single Shift
404
18.7.
Schur s Triangularization
405
18.8.
The Francis Algorithm
409
18.8.1.
Francis Iteration of
Degree One
409
18.8.2.
Francis Iteration of Degree Two
413
18.9.
Computing Eigenvectors
420
18.9.1.
Hessenberg
Inverse Iteration
421
18.10.
Computing Both Eigenvalues
and Their Corresponding
Eigenvectors
423
18.11.
Sensitivity of Eigenvalues to
Perturbations
424
18.11.1.
Sensitivity of Eigenvectors
427
18.12.
Chapter Summary
428
18.13.
Problems
430
18.13.1.
MATLAB
Problems
432
19.
The Symmetric Eigenvalue Problem
439
19.1.
The Spectral Theorem and Properties
of a Symmetric Matrix
439
19.1.1.
Properties of a Symmetric Matrix
440
19.2.
The Jacobi Method
440
19.2.1.
Computing Eigenvectors Using
the Jacobi Iteration
444
19.2.2.
The Cyclic-by-Row jacobi
Algorithm
444
19.3.
The Symmetric QR Iteration Method
446
19.3.1.
Tridiagonal Reduction of a
Symmetric Matrix
449
19.3.2.
Orthogonal Transformation to a
Diagonal Matrix
451
19.4.
The Symmetric Francis Algorithm
452
19.4.1.
Theoretical Overview and
Efficiency
453
19.5.
The Bisection Method
453
19.5.1.
Efficiency
457
19.5.2.
Matrix A Is Not Unreduced
457
19.6.
The Divide-and-Conquer Method
458
19.6.1.
Using dconquer
461
19.7.
Chapter Summary
461
19.8.
Problems
463
19.8.1.
MATLAB
Problems
465
20.
Basic Iterative Methods
469
20.1.
Jacobi Method
469
20.2.
The Gauss-Seidel Iterative Method
470
20.3.
The
SOR
Iteration
471
20.4.
Convergence of the Basic Iterative
Methods
473
20.4.1.
Matrix Form of the Jacobi
Iteration
473
20.4.2.
Matrix Form of the Gauss-Seidel
Iteration
473
20.4.3.
Matrix Form for
SOR
474
20.4.4.
Conditions Guaranteeing
Convergence
474
20.4.5.
The Spectral Radius and Rate of
Convergence
476
20.4.6.
Convergence of the Jacobi and
Gauss-Seidel Methods for
Diagonally Dominant Matrices
477
20.4.7.
Choosing
ω
for
SOR
478
20.5.
Application: Poisson s Equation
478
20.6.
Chapter Summary
481
20.7.
Problems
483
20.7.1.
MATLAB
Problems
486
21.
Krylov Subspace Methods
491
21.1.
Large, Sparse Matrices
491
21.1.1.
Storage of Sparse Matrices
492
21.2.
The
CG
Method
493
21.2.1.
The Method of Steepest
Descent
493
21.2.2.
From Steepest Descent to
CG 497
21.2.3.
Convergence
501
21.3.
Preconditioning
501
21.4.
Preconditioning for
CG 503
21.4.1.
Incomplete Cholesky
Decomposition
503
21.4.2.
SSOR Preconditioner
506
21.5.
Krylov Subspaces
508
21.6.
The
Arnoldi
Method
509
21.6.1.
An Alternative Formulation of
the
Arnoldi
Decomposition
511
21.7.
GMRES
512
21.7.1.
Preconditioned GMRES
514
21.8.
The Symmetric Lanczos Method
516
21.8.1.
Loss of Orthogonality with the
Lanczos Process
516
21.9.
The MINRES Method
519
21.10.
Comparison of Iterative Methods
520
21.11.
Poisson s Equation Revisited
521
21.12.
The Biharmonic Equation
523
21.13.
Chapter Summary
524
21.14.
Problems
526
21.14.1.
MATLAB
Problems
528
22.
Large Sparse Eigenvalue Problems
533
22.1.
The Power Method
533
22.2.
Eigenvalue Computation Using the
Arnoldi
Process
534
22.2.1.
Estimating Eigenvalues Without
Restart or Deflation
535
22.2.2.
Estimating Eigenvalues Using
Restart
536
22.2.3.
A Restart Method Using
Deflation
537
22.2.4.
Restart Strategies
539
22.3.
The Implicitly Restarted
Arnoldi
Method
540
22.3.1.
Convergence of the
Arnoldi
Iteration
544
22.4.
Eigenvalue Computation Using the
Lanczos Process
544
22.4.1.
Mathematically Provable
Properties
546
22.5.
Chapter Summary
547
22.6.
Problems
548
22.6.1.
MATLAB
Problems
548
23.
Computing the Singular Value
Decomposition
551
23.1.
Development of the One-Sided Jacobi
Method for Computing the Reduced
SVD
551
23.1.1.
Stability of Singular Value
Computation
554
23.2.
The One-Sided Jacobi Algorithm
555
23.2.1.
Faster and More Accurate Jacobi
Algorithm
557
23.3.
Transforming a Matrix to
Upper-Bidiagonal Form
558
23.4.
Demmel and
Kahan
Zero-Shift QR
Downward Sweep Algorithm
559
23.5.
Chapter Summary
565
23.6.
Problems
565
23.6.1.
MATLAB
Problems
566
A. Complex Numbers
569
A.1. Constructing the Complex
Numbers
569
A.2. Calculating with Complex
Numbers
570
A.3. Geometric Representation of
С
571
A.4. Complex Conjugate
571
A.5. Complex Numbers in
MATLAB
573
A.6. Euler s Formula
575
A.7. Problems
575
A.7.1.
MATLAB
Problems
576
B. Mathematical Induction
579
B.1. Problems
581
C. Chebyshev Polynomials
583
C.1. Definition
583
C.2. Properties
584
C.3. Problems
584
C.3.1.
MATLAB
Problems
585
Glossary
587
Bibliography
595
Index
597
Numerical Linear Algebra with Applications
Using
MATLAB
By William Ford, University of the Pacific, Stockton, California
A text for students and professionals in engineering and science who need
to compute solutions to problems involving linear algebra.
Designed for those who want to gain a practical knowledge of modern computational
techniques for the numerical solution of linear algebra problems, Numerical Linear
Algebra with Applications contains all the material necessary for an advanced
undergraduate or a first-year graduate course. Introductory chapters present the
linear algebra necessary for reading the remainder of the text, so a prior course in
linear algebra is not required. This book presents careful proofs of major results
or provides references, and written exercises complement the theory. The primary
emphasis, though, is to enable the reliable
щ0Мкт
of solutions to practical
problems. This book presents algorithms
u^^Äjdocode,
and all are implemented
using
MATLAB
in a library provided to you, |^|re many computational exercises
for which
MATLAB
is the ¡deal vehicle.
-$
ľ
Key Features
•
A prior course in applied or theoretical linear algebra is not needed after studying
the first six chapters
•
Detailed presentation of necessary theory
•
Case studies of engineering and scientific applications
•
Doable written exercises that support or enhance the theory or carefully
introduce additional algorithms
•
Many computational problems that use already-developed software or require
the development of
MATLAB
code
|
| any_adam_object | 1 |
| author | Ford, William |
| author_facet | Ford, William |
| author_role | aut |
| author_sort | Ford, William |
| author_variant | w f wf |
| building | Verbundindex |
| bvnumber | BV041477109 |
| classification_rvk | SK 220 SK 915 ST 601 |
| ctrlnum | (OCoLC)813210746 (DE-599)BVBBV041477109 |
| 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 | Informatik Mathematik |
| edition | 1. ed. |
| format | Book |
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| id | DE-604.BV041477109 |
| illustrated | Not Illustrated |
| indexdate | 2025-02-20T06:44:31Z |
| institution | BVB |
| isbn | 012394435X 9780123944351 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026923148 |
| oclc_num | 813210746 |
| open_access_boolean | |
| owner | DE-739 DE-92 DE-11 DE-862 DE-BY-FWS DE-573 DE-20 |
| owner_facet | DE-739 DE-92 DE-11 DE-862 DE-BY-FWS DE-573 DE-20 |
| physical | XXVI, 602 S. Ill., graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | Elsevier |
| record_format | marc |
| spellingShingle | Ford, William Numerical linear algebra with applications using matlab Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Online-Ressource (DE-588)4511937-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| subject_GND | (DE-588)4042805-9 (DE-588)4329066-8 (DE-588)4511937-5 (DE-588)4035811-2 |
| title | Numerical linear algebra with applications using matlab |
| title_auth | Numerical linear algebra with applications using matlab |
| title_exact_search | Numerical linear algebra with applications using matlab |
| title_full | Numerical linear algebra with applications using matlab by William Ford |
| title_fullStr | Numerical linear algebra with applications using matlab by William Ford |
| title_full_unstemmed | Numerical linear algebra with applications using matlab by William Ford |
| title_short | Numerical linear algebra with applications |
| title_sort | numerical linear algebra with applications using matlab |
| title_sub | using matlab |
| topic | Numerische Mathematik (DE-588)4042805-9 gnd MATLAB (DE-588)4329066-8 gnd Online-Ressource (DE-588)4511937-5 gnd Lineare Algebra (DE-588)4035811-2 gnd |
| topic_facet | Numerische Mathematik MATLAB Online-Ressource Lineare Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026923148&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=026923148&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT fordwilliam numericallinearalgebrawithapplicationsusingmatlab |
Inhaltsverzeichnis
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