krylov {fastmatrix}

Computes a Krylov matrix

Description

Given \bold{A} an n by n real matrix and an n-vector \bold{b}, this function constructs the Krylov matrix \bold{K}, where

\bold{K} = [\bold{b},\bold{Ab},\dots,\bold{A}^{m-1}\bold{b}].

Usage

krylov(a, b, m = ncol(a))

Arguments

a

a numeric square matrix of order n by n for which the Krylov matrix is to be computed.

b

a numeric vector of length n.

m

length of the Krylov sequence.

Value

Returns an n by m matrix.

Examples

a <- matrix(c(1, 3, 2, -5, 1, 7, 1, 5, -4), ncol = 3, byrow = TRUE)
b <- c(1, 1, 1)
k <- krylov(a, b, m = 4)
k