| Title: | Preconditioned Conjugate Gradient Algorithm for solving Ax=b |
|---|---|
| Description: | The package solves linear system of equations Ax=b by using Preconditioned Conjugate Gradient Algorithm where A is real symmetric positive definite matrix. A suitable preconditioner matrix may be provided by user. This can also be used to minimize quadratic function (x'Ax)/2-bx for unknown x. |
| Authors: | B N Mandal <[email protected]> and Jun Ma <[email protected]> |
| Maintainer: | B N Mandal <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.1 |
| Built: | 2025-01-23 05:25:20 UTC |
| Source: | https://github.com/cran/pcg |
The function solves linear system of equations Ax=b by Preconditioned Conjugate Gradient algorithm. Here matrix A must be real symmetric and positive definite. This can also be used to minimize the quadractic function (x'Ax)/2-bx.
pcg(A, b, M, maxiter = 1e+05, tol = 1e-06)pcg(A, b, M, maxiter = 1e+05, tol = 1e-06)
A |
A is real symmetric positive definite matrix of order n x n. |
b |
b is a vector of order n x 1. |
M |
Optionally a suitable preconditioner matrix specified by user |
maxiter |
Maximum number of iterations |
tol |
Tolerance for convergence of the solution |
A vector of order n x 1
The algorithm does not check for symmetricity and positive definiteness of matrix A. Please ensure these conditions yourself.
B N Mandal and Jun Ma
Barrett, R., M. Berry, T. F. Chan, et al., (1994). Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia.
A=matrix(rnorm(100*100,mean=10,sd=2),100,100) A=t(A)%*%A b=rnorm(100) pcg(A,b)A=matrix(rnorm(100*100,mean=10,sd=2),100,100) A=t(A)%*%A b=rnorm(100) pcg(A,b)