I have a fairly large matrix (250*250) in symbolic form in MATLAB. Matrix is square invertible with size multiple of 2. I have to calculate the first two elements of the first two rows of its inverse (i.e. first 2x2 block). Matrix is very large and in symbolic form ,so, Matlab is not able to calculate the whole inverse due to time limitations. I have tried guassian elimination, LU factorization, block wise inverse technique. I have also tried the simple method of cofactors and determinent. In all the cases the problem is the same: very long time in the range of hours. Can anyone suggest some technique?
Hi, perhaps another solution is to solve two linear systems of the form A.x=b where b is set to (1,0,0...0) and (0,1,0,0....0) respectively, just to obtain the first two columns of the inverse of A.
because you told that Matrix is in symbolic Form. Instead if it was numeric then Matlab is sound!
Why do you need the inverse? I don't know of many instances where you actually need the inverse of a matrix.
There is a [1] master thesis that discusses taking partial inverse of a sparse matrix, a matrix with most of its entries as zero. [2] and [3] discuss principal pivot transforms. There is R language implementation in [2].
1. Rouet, F. R. Partial computation of the inverse of a large sparse matrix-application to astrophysics. INP-ENSEEEIHT/IRIT, http://rouet. perso. enseeiht. fr/report. pdf, 2009.
2. de Leeuw, Jan. "Exceedingly Simple Principal Pivot Transforms."
3. Tsatsomeros, Michael J. "Principal pivot transforms: properties and applications." Linear Algebra and its Applications 307.1-3 (2000): 151-165.
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