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>

```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

```

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