Re: Inverse of a Big Matrix

*To*: mathgroup at smc.vnet.net*Subject*: [mg96894] Re: Inverse of a Big Matrix*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Thu, 26 Feb 2009 08:02:51 -0500 (EST)

On 2/25/09 at 4:06 AM, gregory.lypny at videotron.ca (Gregory Lypny) wrote: >I'm computing the inverse of a big matrix, 500 x 500. Well, maybe >not that big, but I'm getting the error message >"General::luc: Result for `1` of badly conditioned matrix `2` may >contain significant numerical errors. >>" >and I'm wondering if anyone can suggest a workaround. All I can say >is that the determinant is very small (-4.327475016428501*10^-1947), If the determinant is that small, why do you think it isn't truly 0? Recall, a matrix with a determinant of 0 is singular and has no inverse. In fact, such a small determinant is the reason you are getting a warning about a badly conditioned matrix. If the matrix is singular there is no workaround. But why are you computing the inverse? Computing the inverse of a general matrix is computationally expensive (a n^3 problem). There are a variety of algorithms for solving matrix problems that avoid explicitly computing a matrix inverse and are much more efficient. Many of these are built in to Mathematica already. >and that I can compute the inverse of various submatrices of size >100 x100. Being able to compute the inverse of submatrices of some given matrix says nothing about whether the given matrix is singular or not.