public interface IterativeLinearSystemSolver
Preconditionercan improve the rate of convergence of an iterative method. A preconditioner transforms a linear system into one that is equivalent in the sense that it has the same solution. The transformed system has more favorable spectral properties which affect convergence rate. In particular, a preconditioner M approximates the coefficient matrix A, and the transformed system is easier to solve. For example,
M-1Ax = M-1bhas the same solution as the original system Ax = b. The spectral properties of its coefficient matrix M-1A may be more favorable. Another way of preconditioning a system is
M1-1AM2-1(M2x) = M1-1bThe matrices M1 and M2 are called left- and right preconditioners respectively. There are 3 kinds of preconditioning: left, right, or split. Left-preconditioning leaves M2 as
IdentityPreconditioner. Similarly, right-preconditioning leaves M1 as
|Modifier and Type||Interface and Description|
This is the solution to a system of linear equations using an iterative solver.
|Modifier and Type||Method and Description|
Solves iteratively Ax = b until the solution converges, i.e., the norm of residual (b - Ax) is less than or equal to the threshold.
IterativeLinearSystemSolver.Solution solve(LSProblem problem, IterationMonitor<Vector> monitor) throws ConvergenceFailure
Ax = buntil the solution converges, i.e., the norm of residual (b - Ax) is less than or equal to the threshold.
problem- a system of linear equations
monitor- an iteration monitor
ConvergenceFailure- if the algorithm fails to converge
Copyright © 2010-2018 Numerical Method Incorporation Limited. All Rights Reserved.