Muutke küpsiste eelistusi

First Course in Numerical Methods [Pehme köide]

3.82/5 (29 hinnangut Goodreads-ist)
,
  • Formaat: Paperback, 574 pages, kõrgus x laius x paksus: 229x152x30 mm, kaal: 990 g, Illustrations
  • Sari: Computational Science and Engineering Series 7
  • Ilmumisaeg: 30-Jun-2011
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898719976
  • ISBN-13: 9780898719970
Teised raamatud teemal:
First Course in Numerical MethodsSuurem pilt
  • Formaat: Paperback, 574 pages, kõrgus x laius x paksus: 229x152x30 mm, kaal: 990 g, Illustrations
  • Sari: Computational Science and Engineering Series 7
  • Ilmumisaeg: 30-Jun-2011
  • Kirjastus: Society for Industrial & Applied Mathematics,U.S.
  • ISBN-10: 0898719976
  • ISBN-13: 9780898719970
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780898719970.html
Märksõnad:
A First Course in Numerical Methods is designed for students and researchers who seek practical knowledge of modern techniques in scientific computing. Avoiding encyclopedic and heavily theoretical exposition, the book provides an in-depth treatment of fundamental issues and methods, the reasons behind the success and failure of numerical software, and fresh and easy-to-follow approaches and techniques. The authors focus on current methods, issues, and software while providing a comprehensive theoretical foundation, enabling those who need to apply the techniques to successfully design solutions to nonstandard problems. The book also illustrates algorithms using the programming environment of MATLAB(R), with the expectation that the reader will gradually become proficient in it while learning the material covered in the book. A variety of exercises are provided within each chapter along with review questions aimed at self-testing. The book takes an algorithmic approach, focusing on techniques that have a high level of applicability to engineering, computer science, and industrial mathematics.
List of Figures
xi
List of Tables
xix
Preface xxi
1 Numerical Algorithms
1(16)
1.1 Scientific computing
1(2)
1.2 Numerical algorithms and errors
3(6)
1.3 Algorithm properties
9(5)
1.4 Exercises
14(1)
1.5 Additional notes
15(2)
2 Roundoff Errors
17(22)
2.1 The essentials
17(4)
2.2 Floating point systems
21(5)
2.3 Roundoff error accumulation
26(3)
2.4 The IEEE standard
29(3)
2.5 Exercises
32(4)
2.6 Additional notes
36(3)
3 Nonlinear Equations in One Variable
39(26)
3.1 Solving nonlinear equations
39(4)
3.2 Bisection method
43(2)
3.3 Fixed point iteration
45(5)
3.4 Newton's method and variants
50(5)
3.5 Minimizing a function in one variable
55(3)
3.6 Exercises
58(6)
3.7 Additional notes
64(1)
4 Linear Algebra Background
65(28)
4.1 Review of basic concepts
65(8)
4.2 Vector and matrix norms
73(5)
4.3 Special classes of matrices
78(2)
4.4 Singular values
80(3)
4.5 Examples
83(6)
4.6 Exercises
89(3)
4.7 Additional notes
92(1)
5 Linear Systems: Direct Methods
93(48)
5.1 Gaussian elimination and backward substitution
94(6)
5.2 LU decomposition
100(5)
5.3 Pivoting strategies
105(5)
5.4 Efficient implementation
110(4)
5.5 The Cholesky decomposition
114(3)
5.6 Sparse matrices
117(5)
5.7 Permutations and ordering strategies
122(5)
5.8 Estimating errors and the condition number
127(6)
5.9 Exercises
133(6)
5.10 Additional notes
139(2)
6 Linear Least Squares Problems
141(26)
6.1 Least squares and the normal equations
141(10)
6.2 Orthogonal transformations and QR
151(6)
6.3 Householder transformations and Gram-Schmidt orthogonalization
157(6)
6.4 Exercises
163(3)
6.5 Additional notes
166(1)
7 Linear Systems: Iterative Methods
167(52)
7.1 The need for iterative methods
167(6)
7.2 Stationary iteration and relaxation methods
173(6)
7.3 Convergence of stationary methods
179(3)
7.4 Conjugate gradient method
182(9)
7.5 Krylov subspace methods
191(13)
7.6 Multigrid methods
204(6)
7.7 Exercises
210(8)
7.8 Additional notes
218(1)
8 Eigenvalues and Singular Values
219(32)
8.1 The power method and variants
219(10)
8.2 Singular value decomposition
229(7)
8.3 General methods for computing eigenvalues and singular values
236(9)
8.4 Exercises
245(4)
8.5 Additional notes
249(2)
9 Nonlinear Systems and Optimization
251(44)
9.1 Newton's method for nonlinear systems
251(7)
9.2 Unconstrained optimization
258(13)
9.3 Constrained optimization
271(15)
9.4 Exercises
286(7)
9.5 Additional notes
293(2)
10 Polynomial Interpolation
295(36)
10.1 General approximation and interpolation
295(3)
10.2 Monomial interpolation
298(4)
10.3 Lagrange interpolation
302(4)
10.4 Divided differences and Newton's form
306(7)
10.5 The error in polynomial interpolation
313(3)
10.6 Chebyshev interpolation
316(3)
10.7 Interpolating also derivative values
319(4)
10.8 Exercises
323(7)
10.9 Additional notes
330(1)
11 Piecewise Polynomial Interpolation
331(34)
11.1 The case for piecewise polynomial interpolation
331(2)
11.2 Broken line and piecewise Hermite interpolation
333(4)
11.3 Cubic spline interpolation
337(7)
11.4 Hat functions and B-splines
344(5)
11.5 Parametric curves
349(4)
11.6 Multidimensional interpolation
353(6)
11.7 Exercises
359(4)
11.8 Additional notes
363(2)
12 Best Approximation
365(18)
12.1 Continuous least squares approximation
366(4)
12.2 Orthogonal basis functions
370(3)
12.3 Weighted least squares
373(4)
12.4 Chebyshev polynomials
377(2)
12.5 Exercises
379(3)
12.6 Additional notes
382(1)
13 Fourier Transform
383(26)
13.1 The Fourier transform
383(5)
13.2 Discrete Fourier transform and trigonometric interpolation
388(8)
13.3 Fast Fourier transform
396(9)
13.4 Exercises
405(1)
13.5 Additional notes
406(3)
14 Numerical Differentiation
409(32)
14.1 Deriving formulas using Taylor series
409(4)
14.2 Richardson extrapolation
413(2)
14.3 Deriving formulas using Lagrange polynomial interpolation
415(5)
14.4 Roundoff and data errors in numerical differentiation
420(6)
14.5 Differentiation matrices and global derivative approximation
426(8)
14.6 Exercises
434(4)
14.7 Additional notes
438(3)
15 Numerical Integration
441(40)
15.1 Basic quadrature algorithms
442(4)
15.2 Composite numerical integration
446(8)
15.3 Gaussian quadrature
454(8)
15.4 Adaptive quadrature
462(7)
15.5 Romberg integration
469(3)
15.6 Multidimensional integration
472(3)
15.7 Exercises
475(4)
15.8 Additional notes
479(2)
16 Differential Equations
481(58)
16.1 Initial value ordinary differential equations
481(4)
16.2 Euler's method
485(8)
16.3 Runge-Kutta methods
493(7)
16.4 Multistep methods
500(7)
16.5 Absolute stability and stiffness
507(8)
16.6 Error control and estimation
515(5)
16.7 Boundary value ODEs
520(4)
16.8 Partial differential equations
524(7)
16.9 Exercises
531(6)
16.10 Additional notes
537(2)
Bibliography 539(4)
Index 543
Uri Ascher is a Professor of Computer Science at the University of British Columbia in Vancouver, Canada. He has previously co-authored three other books, published by SIAM, as well as many research papers in the general area of numerical methods and their applications. He is a SIAM Fellow and a recipient of the CAIMS Research Prize. Chen Greif is an Associate Professor of Computer Science at the University of British Columbia in Vancouver, Canada. His research interests are in the field of scientific computing, with specialization in numerical linear algebra. He is currently an associate editor of the SIAM Journal on Scientific Computing.