文档介绍：“dqbjV
2007/5/15
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Germund Dahlquist Ake˚ Bj¨orck
Royal Institute of Technology Link¨oping University
Numerical Methods
in
puting
Volume I
(Working copy, May 15, 2007)
siam
c This material is the property of the authors and is for the sole and exclusive use
of the students enrolled in specific courses. It is not to be sold, reproduced, or
generally distributed.
“dqbjV
2007/5/15
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“dqbjV
2007/5/15
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Contents
Preface xv
1 Principles of Numerical Calculations 1
Ideas and Concepts . . . . . . . . . . . . . . . . . . . . 1
Introduction . . . . . . . . . . . . . . . . . . . . . . 1
Fixed Point Iteration . . . . . . . . . . . . . . . . . 2
Newton’s Method . . . . . . . . . . . . . . . . . . . 5
Linearization and Extrapolation . . . . . . . . . . . 7
Finite Difference Approximations . . . . . . . . . . . 10
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Problems puter Exercises . . . . . . . . . . . . . . . . . . . . . 15
Some Numerical Algorithms . . . . . . . . . . . . . . . . . . . . 16
Solving a Quadratic Equation . . . . . . . . . . . . . 16
Recurrence Relations . . . . . . . . . . . . . . . . . 17
Divide-and-Conquer Strategy . . . . . . . . . . . . . 20
Power Series Expansions . . . . . . . . . . . . . . . . 21
Review Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Problems puter Exercises . . . . . . . . . . . . . . . . . . . . . 23
putations . . . . . . . . . . . . . . . . . . . . . . . . 25
Matrix Multiplication . . . . . . . . . . . . . . . . . 26
Solving Linear Systems by LU Factorization . . . . 28
The Linear Least Squares Problem . . . . . . . . . . 37
The Singular Value position . . . . . . . . . . 41
Sparse Matrices and Iterative Methods . . . . . . . 44
Software for putations . . . . . . . . . . 47