cg

Solve linear systems using the conjugate gradients method

Description

Conjugate gradients (CG) method is an iterative algorithm for solving linear systems with positive definite coefficient matrices.

Usage

cg(a, b, maxiter = 200, tol = 1e-7)

Arguments

Argument	Description
a	a symmetric positive definite matrix containing the coefficients of the linear system.
b	a vector of right-hand sides of the linear system.
maxiter	the maximum number of iterations. Defaults to 200
tol	tolerance level for stopping iterations.

Value

a vector with the approximate solution, the iterations performed are returned as the attribute 'iterations'.

Seealso

jacobi , seidel , solve

References

Golub, G.H., Van Loan, C.F. (1996). Matrix Computations , 3rd Edition. John Hopkins University Press.

Hestenes, M.R., Stiefel, E. (1952). Methods of conjugate gradients for solving linear equations. Journal of Research of the National Bureau of Standards 49 , 409-436.

Examples

a <- matrix(c(4,3,0,3,4,-1,0,-1,4), ncol = 3)
b <- c(24,30,-24)
z <- cg(a, b)
z # converged in 3 iterations