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pbdDMAT (version 0.2-3)

Expm: Matrix Exponentiation

Description

Routines for matrix exponentiation.

Usage

## S3 method for class 'ddmatrix':
expm(x)
## S3 method for class 'matrix':
expm(x)

Arguments

x
A numeric matrix or a numeric distributed matrix.

Value

  • Returns a distributed matrix.

Details

Formally, the exponential of a square matrix X is a power series: $expm(x) = X/1! + X^2/2! + X^3/3! + \dots$ 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).

References

Matrix exponentiation using Pade' approximations and scaling and squaring from: "New Scaling and Squaring Algorithm for the Matrix Exponential" Awad H. Al-Mohy and Nicholas J. Higham, August 2009

See Also

Arithmetic, Reductions, MatMult, LinAlg