Solve a matrix using iterative methods

Solve a matrix using iterative methods.

jacobi(A, b, tol = 1e-06, maxiter = 100)

gaussseidel(A, b, tol = 1e-06, maxiter = 100)

cgmmatrix(A, b, tol = 1e-06, maxiter = 100)

Arguments

A	a square matrix representing the coefficients of a linear system
b	a vector representing the right-hand side of the linear system
tol	is a number representing the error tolerence
maxiter	is the maximum number of iterations

Value

the solution vector

Details

jacobi finds the solution using Jacobi iteration. Jacobi iteration depends on the matrix being diagonally-dominate. The tolerence is specified the norm of the solution vector.

gaussseidel finds the solution using Gauss-Seidel iteration. Gauss-Seidel iteration depends on the matrix being either diagonally-dominate or symmetric and positive definite.

cgmmatrix finds the solution using the conjugate gradient method. The conjugate gradient method depends on the matrix being symmetric and positive definite.

See also

Other linear: choleskymatrix(), detmatrix(), gdls(), invmatrix(), lumatrix(), refmatrix(), rowops, tridiagmatrix(), vecnorm()

Examples

A <- matrix(c(5, 2, 1, 2, 7, 3, 3, 4, 8), 3)
b <- c(40, 39, 55)
jacobi(A, b)
#> [1] 4 1 6