Solve a matrix using iterative methods

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Description

Solve a matrix using iterative methods.

Usage

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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

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.

Value

the solution vector

See Also

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

Examples

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

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