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Computational simulation of scientific phenomena and engineering problems often depends on solving linear systems with a large number of unknowns. This book gives insight into the construction of iterative methods for the solution of such systems and helps the reader to select the best solver for a given class of problems. The emphasis is on the main ideas and how they have led to efficient solvers such as CG, GMRES, and BI-CGSTAB. The author also explains the main concepts behind the construction of preconditioners. The reader is encouraged to gain experience by analysing numerous examples that illustrate how best to exploit the methods. The book also hints at many open problems and as such it will appeal to established researchers. There are many exercises that motivate the material and help students to understand the essential steps in the analysis and construction of algorithms.

Iterative methods (Mathematics) --- Numerical solutions of algebraic equations --- 519.61 --- 681.3*G13 --- 519.61 Numerical methods of algebra --- Numerical methods of algebra --- 681.3*G13 Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Numerical linear algebra: conditioning; determinants; Eigenvalues; error analysis; linear systems; matrix inversion; pseudoinverses; sparse and very largesystems --- Linear systems. --- Itération (Mathématiques) --- Systèmes linéaires --- Linear systems --- Systems, Linear --- Differential equations, Linear --- System theory --- Iteration (Mathematics) --- Numerical analysis

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This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices.Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for p

Algebras, Linear --- Numerical calculations --- Parallel processing (Electronic computers) --- Parallel algorithms --- Algorithms --- High performance computing --- Multiprocessors --- Parallel programming (Computer science) --- Supercomputers --- Numerical analysis --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Algèbre linéaire --- Calculs numériques --- Calculs numériques --- Algèbre linéaire --- Parallélisme (Informatique) --- Parallel algorithms. --- Algebras, Linear. --- Numerical calculations. --- Algorithmes --- Analyse numérique. --- Itération (mathématiques) --- Iterative methods (Mathematics) --- Analyse numérique. --- Itération (mathématiques)