expm: Matrix Exponentiation

In wrathematics/pbdDMAT: 'pbdR' Distributed Matrix Methods

Matrix Exponentiation

Description

Routines for matrix exponentiation.

Usage

expm(x, t = 1, p = 6)

## S4 method for signature 'matrix'
expm(x, t = 1, p = 6)

## S4 method for signature 'ddmatrix'
expm(x, t = 1, p = 6)

Arguments

x	A numeric matrix or a numeric distributed matrix.
t	Scaling parameter for x.
p	Order of the Pade' approximation.

Details

Formally, the exponential of a square matrix X is a power series:

expm(X) = id + X/1! + X^2/2! + X^3/3! + \dots

where the powers on the matrix correspond to matrix-matrix multiplications.

expm() directly computes the matrix exponential of a distributed, dense matrix. The implementation uses Pade' approximations and a scaling-and-squaring technique (see references).

Value

Returns a distributed matrix.

References

"New Scaling and Squaring Algorithm for the Matrix Exponential" Awad H. Al-Mohy and Nicholas J. Higham, August 2009

wrathematics/pbdDMAT documentation built on Oct. 2, 2024, 2:56 p.m.