Table
of Contents for
Solving
Linear Systems
An Analysis of Matrix
Prefactorization Iterative Methods
by Zbigniew
Ignacy
554 pages,
8 x 10 inches, hardcover, smythesewn binding
More
than 230 figures and 140 tables, $89
ISBN
9780971576667
Table of
contents in pdf
Foreword (by
Richard Varga)
Chapter 0
Introduction to
iterative methods and preconditioning 1
Chapter 1
Numerical linear
algebra: background 5
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
PerronFrobenius theory of nonnegative matrices
Diagonally dominant matrices
Power method
1.3 General linear
systems
Direct
methods
Iterative
refinement
Chapter
2 The theory of
matrix splitting 41
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
Chapter
3 Discretization of
partial differential equations 70
3.1
Finitedifference approximations
3.2 Onedimensional problems
Forward
elimination  backward substitution
Backward elimination  forward substitution
3.3
Band matrices
Pentadiagonal
matrices
General
band systems
3.4
Twodimensional problems
Rectangular
geometry
Triangular
geometry
Hexagonal geometry
Reduced
systems
Line orderings
Computational molecules
Irregular
mesh structures
3.5
Test problems
Chapter 4 Standard iterative
methods 129
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
1line
algorithms
2line
algorithms
3line
algorithms
4.4
Results of numerical experiments
Chapter
5 Explicit
prefactorization methods (AGA) 199
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
Chapter 6 Semiexplicit
prefactorization with implicit backward sweep 248
6.1
Matrix notation
6.2
Implementation in mesh structures
Rectangular
geometry
Triangular geometry
Hexagonal geometry
6.3
Numerical experiments
Selfadjoint
problems
Nonselfadjoint
problems
Concluding remarks
Chapter
7 Semiexplicit
prefactorization with implicit forward sweep (OLA) 436
7.1
Implementing OLA methods in mesh structures
Rectangular
geometry
Triangular geometry
Hexagonal geometry
Successive overrelaxation
7.2
Matrix notation
7.3
Numerical experiments
Selfadjoint
problems
Nonselfadjoint
problems
OLA
algorithms: concluding remarks
7.4
Final discussion
Chapter
8 Advances
in solving linear control systems 308
8.1
Sylvester equations
The
SORlike method
Numerical experiments
Sylvester equations: conclusion
8.2
Continuoustime algebraic Riccati equations
The
SORlike method
Numerical
experiments
Concluding
remarks
Appendices
Appendix A
Numerical experiments for chapter 4 325
Appendix B Numerical experiments for chapter 5 375
Appendix C
Numerical experiments for chapter 6 473
Appendix
D Numerical experiments for chapter 7 496
Bibliography 529
Index
535
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