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

In fastmatrix: Fast Computation of some Matrices Useful in Statistics

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)

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.

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".

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)

fastmatrix documentation built on Oct. 12, 2023, 5:14 p.m.