文档介绍：1
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.
Contents
Preface xv
1 Principles of Numerical Calculations 1
.................... 1
Introduction...................... 1
FixedPointIteration................. 2
Newton’sMethod................... 5
Linearization and Extrapolation . . . . . . . . . . . 7
Finite Difference Approximations . . . . . . . . . . . 10
ReviewQuestions.............................. 14
puterExercises..................... 15
SomeNumericalAlgorithms.................... 16
SolvingaQuadraticEquation............. 16
RecurrenceRelations................. 17
Divide-and-ConquerStrategy............. 20
PowerSeriesExpansions................ 21
ReviewQuestions.............................. 23
puterExercises..................... 23
putations........................ 25
MatrixMultiplication................. 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
ReviewQuestions.............................. 48
puterExercises..................... 49
Numerical Solution of Differential Equations . . . . . . . . . . . 50
Euler’sMethod..................... 50
AnIntroductoryExample............... 52
urateMethods........... 55
AdaptiveChoiceofStepSize............. 57
ReviewQuestions.............................. 59
puterExercises..................