showstat

Christopher2222 — Fri, 14 Oct 2011 03:11:47 Z

Not sure what algorithm Maple uses but you could use showstat() to try to determine which one.

showstat(LinearAlgebra[MatrixInverse])

singular vectors and the SVD

pagan — Fri, 14 Oct 2011 03:53:24 Z

I suppose that you mean for floating-point, not for the exact symbolic case.

It uses the singular value decomposition. See also the first application example described here.

You can view the code that accomplishes this. Using Maple 15

showstat((LinearAlgebra::LA_Main)::`MatrixInverse/pseudo`,34..57);

In Maple 11, the relevent code can be seen by issuing these commands

kernelopts(opaquemodules=false):
showstat(LinearAlgebra:-LA_Main:-`MatrixInverse/pseudo`,34..57);

The code looks more complicated than it is, just because some care is being taken to keep down unnecessary copies in various cases like n>m, m>n, etc.

It also computes a "proviso" of correctness. This is computed as a ratio of the r'th ordered singular value and the largest singular value, where r the rank of the Matrix is determined according to how many of the ordered singular values have a ratio w.r.t the largest that is greater than some tolerance that depends upon Digits. This is akin to how the Rank command determines r for float Matrices.

MaplePrimes - answers and comments on Question, Algorithm used by Maple function 'MatrixInverse' for calculating pseudo inverse of matrix

showstat

singular vectors and the SVD