fastmatrix (version 0.5-7721)

power.method: Power method to approximate dominant eigenvalue and eigenvector

Description

The power method seeks to determine the eigenvalue of maximum modulus, and a corresponding eigenvector.

Usage

power.method(x, only.value = FALSE, maxiter = 100, tol = 1e-8)

Value

When only.value is not true, as by default, the result is a list with components

"value" and "vector". Otherwise only the dominan eigenvalue is returned. The performed number of iterations to reach convergence is returned as attribute "iterations".

Arguments

x

a symmetric matrix.

only.value

if TRUE, only the dominant eigenvalue is returned, otherwise both dominant eigenvalue and eigenvector are returned.

maxiter

the maximum number of iterations. Defaults to 100

tol

a numeric tolerance.

See Also

eigen for eigenvalues and eigenvectors computation.

Examples

n <- 1000
x <- .5 * diag(n) + 0.5 * matrix(1, nrow = n, ncol = n)

# dominant eigenvalue must be (n + 1) / 2
z <- power.method(x, only.value = TRUE)