Numerical analysis: mathematics of scientific computing
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, RI
American Math. Soc.
2002
|
| Ausgabe: | 3. ed. |
| Schriftenreihe: | Pure and applied undergraduate texts
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Originally published: 3. ed. Pacific Grove, CA : Brooks/Cole, c2002 |
| Beschreibung: | XIV, 788 S. graph. Darst. |
| ISBN: | 9780821847886 |
Internformat
MARC
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| 020 | |a 9780821847886 |9 978-0-8218-4788-6 | ||
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| 100 | 1 | |a Kincaid, David |d 1942- |e Verfasser |0 (DE-588)121384152 |4 aut | |
| 245 | 1 | 0 | |a Numerical analysis |b mathematics of scientific computing |c David Kincaid ; Ward Cheney |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Providence, RI |b American Math. Soc. |c 2002 | |
| 300 | |a XIV, 788 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pure and applied undergraduate texts |v 2 | |
| 490 | 0 | |a The Sally series | |
| 500 | |a Originally published: 3. ed. Pacific Grove, CA : Brooks/Cole, c2002 | ||
| 650 | 4 | |a Numerical analysis | |
| 650 | 0 | 7 | |a Numerische Mathematik |0 (DE-588)4042805-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Numerische Mathematik |0 (DE-588)4042805-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Cheney, Elliott W. |d 1929- |e Verfasser |0 (DE-588)122199545 |4 aut | |
| 830 | 0 | |a Pure and applied undergraduate texts |v 2 |w (DE-604)BV035489189 |9 2 | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017372587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-017372587 | ||
Datensatz im Suchindex
| _version_ | 1804138904136187904 |
|---|---|
| adam_text | Contents
Numerical Analysis: What Is It?
1
Mathematical Preliminaries
3
1.0
Introduction
3
1.1
Basic Concepts and Taylor s Theorem
3
1.2
Orders of Convergence and Additional Basic Concepts
15
1.3
Difference Equations
28
Computer Arithmetic
37
2.0
Introduction
37
2.1
Floating-Point Numbers and Roundoff Errors
37
2.2
Absolute and Relative Errors: Loss of Significance
55
2.3
Stable and Unstable Computations: Conditioning
64
Solution of Nonlinear Equations
73
3.0
Introduction
73
3.1
Bisection (Interval Halving) Method
74
3.2
Newton s Method
81
3.3
Secant Method
93
3.4
Fixed Points and Functional Iteration
100
3.5
Computing Roots of Polynomials
109
3.6
Homotopy and Continuation Methods
130
Solving Systems of Linear Equations
139
4.0
Introduction
139
4.1
Matrix Algebra
140
4.2
LU
and Cholesky Factorizations
149
4.3
Pivoting and Constructing an Algorithm
163
4.4
Norms and the Analysis of Errors
186
4.5
Neumann Series and Iterative Refinement
197
4.6
Solution of Equations by Iterative Methods
207
4.7
Steepest Descent and Conjugate Gradient Methods
232
4.8
Analysis of Roundoff Error in the Gaussian Algorithm
245
5
Selected Topics in Numerical Linear Algebra
254
5.0
Review of Basic Concepts
254
5.1
Matrix Eigenvalue Problem: Power Method
257
5.2
Schur s and Gershgorin s Theorems
265
5.3
Orthogonal Factorizations and Least-Squares Problems
273
5.4
Singular-Value Decomposition and
Pseudoinverses
287
5.5
QR-Algorithm of Francis for the Eigenvalue Problem
298
6
Approximating Functions
308
6.0
Introduction
308
6.1
Polynomial Interpolation
308
6.2
Divided Differences
327
6.3
Hermite Interpolation
338
6.4
Spline Interpolation
349
6.5 ß-Splines:
Basic Theory
366
6.6 ß-Splines:
Applications
377
6.7
Taylor Series
388
6.8
Best Approximation: Least-Squares Theory
392
6.9
Best Approximation: Chebyshev Theory
405
6.10
Interpolation in Higher Dimensions
420
6.11
Continued Fractions
438
6.12
Trigonometric Interpolation
445
6.13
Fast Fourier Transform
451
6.14
Adaptive Approximation
460
7
Numerical Differentiation and Integration
465
7.1
Numerical Differentiation and Richardson Extrapolation
465
7.2
Numerical Integration Based on Interpolation
478
7.3
Gaussian Quadrature
492
7.4
Romberg Integration
502
7.5
Adaptive
Quadrature
507
7.6
Sard s Theory of Approximating Functional
513
7.7
Bernoulli Polynomials and the Euler-Madaurin Formula
519
8
Numerical Solution of Ordinary
Differential Equations
524
8.0
Introduction
524
8.1
The Existence and Uniqueness of Solutions
524
8.2
Taylor-Series Method
530
8.3
Runge-Kutta Methods
539
8.4
Multistep Methods
549
8.5
Local and Global Errors: Stability
557
8.6
Systems and Higher-Order Ordinary Differential Equations
565
8.7
Boundary-Value Problems
572
8.8
Boundary-Value Problems: Shooting Methods
581
8.9
Boundary-Value Problems: Finite-Differences
589
8.10
Boundary-Value Problems: Collocation
593
8.11
Linear Differential Equations
597
8.12
Stiff Equations
608
Numerical Solution of Partial Differential Equations
615
9.0
Introduction
615
9.1
Parabolic Equations: Explicit Methods
615
9.2
Parabolic Equations: Implicit Methods
623
9.3
Problems Without Time Dependence: Finite-Differences
629
9.4
Problems Without Time Dependence: Galerkin Methods
634
9.5
First-Order Partial Differential Equations: Characteristics
642
9.6 Quasilinear
Second-Order Equations: Characteristics
650
9.7
Other Methods for Hyperbolic Problems
660
9.8
Multigrid Method
667
9.9
Fast Methods for
Poissons
Equation
676
Linear Programming and Related Topics
681
10.1
Convexity and Linear Inequalities
681
10.2
Linear Inequalities
689
11
103 Linear Programming
695
10.4 The Simplex
Algorithm
700
Optimization
711
П.О
Introduction
711
11.1
One-Variable Case
712
11.2
Descent Methods
716
11.3
Analysis of Quadratic Objective Functions
719
11.4
Quadratic-Fitting Algorithms
721
11.5
Nelder-Mead Algorithm
722
11.6
Simulated Annealing
723
11.7
Genetic Algorithms
724
11.8
Convex Programming
725
11.9
Constrained Minimization
726
11.10
Pareto Optimization
727
An Overview of Mathematical Software
731
Bibliography
745
Index
771
|
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| author | Kincaid, David 1942- Cheney, Elliott W. 1929- |
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| dewey-full | 518 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518 |
| dewey-search | 518 |
| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV035452584 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:35:36Z |
| institution | BVB |
| isbn | 9780821847886 |
| language | English |
| lccn | 2008047389 |
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| physical | XIV, 788 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Pure and applied undergraduate texts |
| series2 | Pure and applied undergraduate texts The Sally series |
| spelling | Kincaid, David 1942- Verfasser (DE-588)121384152 aut Numerical analysis mathematics of scientific computing David Kincaid ; Ward Cheney 3. ed. Providence, RI American Math. Soc. 2002 XIV, 788 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Pure and applied undergraduate texts 2 The Sally series Originally published: 3. ed. Pacific Grove, CA : Brooks/Cole, c2002 Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 s DE-604 Cheney, Elliott W. 1929- Verfasser (DE-588)122199545 aut Pure and applied undergraduate texts 2 (DE-604)BV035489189 2 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017372587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kincaid, David 1942- Cheney, Elliott W. 1929- Numerical analysis mathematics of scientific computing Pure and applied undergraduate texts Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4042805-9 |
| title | Numerical analysis mathematics of scientific computing |
| title_auth | Numerical analysis mathematics of scientific computing |
| title_exact_search | Numerical analysis mathematics of scientific computing |
| title_full | Numerical analysis mathematics of scientific computing David Kincaid ; Ward Cheney |
| title_fullStr | Numerical analysis mathematics of scientific computing David Kincaid ; Ward Cheney |
| title_full_unstemmed | Numerical analysis mathematics of scientific computing David Kincaid ; Ward Cheney |
| title_short | Numerical analysis |
| title_sort | numerical analysis mathematics of scientific computing |
| title_sub | mathematics of scientific computing |
| topic | Numerical analysis Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Numerical analysis Numerische Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017372587&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035489189 |
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