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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>