Matrix
Editions

*serious mathematics, written with the reader in mind*

Prefactorization Iterative Methods

ISBN-13: 9780971576667

554 pages, 8 x 10 inches, hardcover, smythe-sewn binding

More than 230 figures and 140 tables

*Please consider recommending that your university or department librarian order this book. Thank you!*

Foreword by Richard Varga

Chapter 0 Introduction to iterative methods and preconditioning

Chapter 1 Numerical linear algebra: background

1.1 Review of matrix theory

Basic matrix operations

Matrix partitionings

Basic concepts of matrix analysis

Vector norms and matrix norms

Computational work

1.2 Eigenvalues and eigenvectors

Relating norms and eigenvalues

Convergence of vector and matrix sequences

Perron-Frobenius theory of nonnegative matrices

Diagonally dominant matrices

Power method

1.3 General linear systems

Direct methods

Iterative refinement

2.1 General properties of matrix splittings

2.2 Regular splittings

2.3 Nonnegative and weak nonnegative splittings

2.4 Weak and weaker splittings

2.5 Summary

3.1 Finite-difference approximations

3.2 One-dimensional problems

Forward elimination - backward substitution

Backward elimination - forward substitution

3.3 Band matrices

Pentadiagonal matrices

General band systems

3.4 Two-dimensional problems

Rectangular geometry

Triangular geometry

Hexagonal geometry

Reduced systems

Line orderings

Computational molecules

Irregular mesh structures

3.5 Test problems

4.1 General theory of iterative methods

Stopping criteria

Starting vectors

4.2 Point iterative methods

Basic algorithms
Consistent orderings

The successive overrelaxation method (SOR)

Determining the optimum relaxation parameter

Experimental examination of SOR convergence

Computational aspects

4.3 Line iterative methods

1-line algorithms

2-line algorithms

3-line algorithms

4.4 Results of numerical experiments

5.1 Matrix notation

Basic algorithms

AGA algorithms with point modification

AGA algorithms with line modification

Techniques for accelerating convergence

5.2 Implementing prefactorization algorithms in mesh structures

Rectangular geometry

Triangular geometry

Hexagonal geometry

5.3 Results of numerical experiments

6.1 Matrix notation

Modified line methods

6.2 Implementation in mesh structures

Rectangular geometry

Triangular geometry

Hexagonal geometry

6.3 Numerical experiments

Self-adjoint problems

Non-self-adjoint problems

Concluding remarks

7.1 Implementing OLA methods in mesh structures

Rectangular geometry

Triangular geometry

Hexagonal geometry

Successive overrelaxation

7.2 Matrix notation

7.3 Numerical experiments

Self-adjoint problems

Non-self-adjoint problems

OLA algorithms: concluding remarks

7.4 Final discussion

8.1 Sylvester equations

The SOR-like method v
Numerical experiments

Sylvester equations: conclusion

8.2 Continuous-time algebraic Riccati equations

The SOR-like method

Numerical experiments

Concluding remarks