Re: calculating an inverse matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg85304] Re: [mg85273] calculating an inverse matrix*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Tue, 5 Feb 2008 19:41:06 -0500 (EST)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200802051100.GAA28832@smc.vnet.net>*Reply-to*: murray at math.umass.edu

Mathematica docs indicate that Inverse is based upon LAPACK routines. If you look up how LAPACK inverts matrices, you'll see among other possibilities -- there are so many routines in LAPACK! -- the routine SGETRI for finding the inverse inv(A) of a general matrix A. It does this using the LU factorization A = L U of A: it inverts U and then finds inv(A) by solving inv(A) L = inv(U). And to find the LU-factorization, the routine in turn calls GETRF; the latter indeed uses partial pivoting with row interchanges. (LAPACK has variants for double precision and for complex matrices.) Of course for special types of matrices, more particular methods may be used. michael.goossens at gmail.com wrote: > So far I know the method of Gauss-Jordan(with pivot to reduce > instability), but are there other(better) methods to calculate an > inverse matrix? > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**calculating an inverse matrix***From:*"michael.goossens@gmail.com" <michael.goossens@gmail.com>