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

power.method {fastmatrix} | R Documentation

## 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)

[Package fastmatrix version 0.3-819 Index]