matrix.polynomial: Evaluates a real general matrix polynomial

In fastmatrix: Fast Computation of some Matrices Useful in Statistics

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 n by n for which the polinomial is to be computed.
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, coef is a vector of all ones. If the exponent is zero, the identity matrix is returned.

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

fastmatrix documentation built on June 8, 2025, 11:43 a.m.