Arbitrary real power of a matrix by Schur-Pade algorithm

version (4.6 KB) by Nick Higham
Computing an arbitrary real power of a square matrix by a Schur-Pade algorithm.


Updated 24 Feb 2011

View License

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.

Cite As

Nick Higham (2022). Arbitrary real power of a matrix by Schur-Pade algorithm (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2010b
Compatible with any release
Platform Compatibility
Windows macOS Linux

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!