A Preconditioned Minimal Residual Solver for a Class of Linear Operator Equations.

Autor:	Awono, O., Tagoudjeu, J.
Předmět:	FIXED point theory PROBLEM solving POLYNOMIALS STOCHASTIC convergence NEUTRON transport theory OPERATOR theory LINEAR operators
Zdroj:	Computational Methods in Applied Mathematics; 2010, Vol. 10 Issue 2, p119-136, 18p
Abstrakt:	We consider the class of linear operator equations with operators admitting self-adjoint positive definite and m-accretive splitting (SAS). This splitting leads to an ADI-like iterative method which is equivalent to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of a minimal residual algorithm with Symmetric Gauss-Seidel and polynomial preconditioning is then applied to solve the resulting matrix operator equation. Theoretical analysis shows the convergence of the methods, and upper bounds for the decrease rate of the residual are derived. The convergence of the methods is numerically illustrated with the example of the neutron transport problem in 2-D geometry. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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