This graduate-level text examines the practical use of iterative methods in solving large, sparse systems of linear algebraic equations and in resolving multidimensional boundary-value problems. Assuming minimal mathematical background, it profiles the relative merits of several general iterative procedures. Topics include polynomial acceleration of basic iterative methods, Chebyshev and conjugate gradient acceleration procedures applicable to partitioning the linear system into a “red/black” block form, adaptive computational algorithms for the successive overrelaxation (SOR) method, and computational aspects in the use of iterative algorithms for solving multidimensional problems. 1981 edition. 48 figures. 35 tables.

Contenuti:

1. Background on Linear Algebra and Related Topics 2. Background on Basic Iterative Methods 3. Polynomial Acceleration 4. Chebyshev Acceleration 5. An Adaptive Chebyshev Procedure Using Special Norms 6. Adaptive Chebyshev Acceleration 7. Conjugate Gradient Acceleration 8. Special Methods for Red/Black Partitionings 9. Adaptive Procedures for the Successive Overrelaxation Method 10. The Use of Iterative Methods in the Solution of Partial Differential Equations 11. Case Studies 12. The Nonsymmetrizable Case Appendixes Bibliography Index

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