matrix.polynomial {fastmatrix} | R Documentation |
Evaluates a real general matrix polynomial
Description
Given c_0,c_1,\dots,c_n
coefficients of the polynomial and \bold{A}
an n
by n
matrix. This function computes the matrix polynomial
\bold{B} = \sum\limits_{k=0}^n c_k\bold{A}^k,
using Horner's scheme, where \bold{A}^0 = \bold{I}
is the n
by n
identity matrix.
Usage
matrix.polynomial(a, coef = rep(1, power + 1), power = length(coef))
Arguments
a |
a numeric square matrix of order |
coef |
numeric vector containing the coefficients of the polinomial in order of increasing power. |
power |
a numeric exponent (which is forced to be an integer). If provided, |
Value
Returns an n
by n
matrix.
Examples
a <- matrix(c(1, 3, 2, -5, 1, 7, 1, 5, -4), ncol = 3, byrow = TRUE)
cf <- c(3, 1, 2)
b <- matrix.polynomial(a, cf)
b # 3 * diag(3) + a + 2 * a %*% a
b <- matrix.polynomial(a, power = 2)
b # diag(3) + a + a %*% a
[Package fastmatrix version 0.6 Index]