Arbitrary real power of a matrix by Schur-Pade algorithm

Computing an arbitrary real power of a square matrix by a Schur-Pade algorithm.

Description

X = POWERM_PADE(A,P) computes the P'th power X of the matrix A, for arbitrary real P and A with no nonpositive real eigenvalues, by the Schur-Pade algorithm. [X,NSQ,M] = POWERM_PADE(A, P) returns the number NSQ of matrix square roots computed and the degree M of the Pade approximant used.

If A is singular or has any eigenvalues on the negative real axis, a warning message is printed.

Function TEST.M runs a simple test of the codes.

Details on the underlying algorithms can be found in

N. J. Higham and L. Lin. A Schur--Pade algorithm for fractional powers of a matrix. MIMS EPrint 2010.91, Manchester Institute for Mathematical Sciences, The University of Manchester, UK, Oct. 2010; revised Feb. 2011.
http://eprints.ma.man.ac.uk/1589/

• MATLAB release: MATLAB 7.11 (2010b)