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Fast Pentadiagonal System Solver

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23 Mar 2004 (Updated )

Solves symmetric and asymmetric pentadiagonal systems.

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Description

Solves the problem Ax=b when A is pentadiagonal (5-banded) and strongly nonsingular. This is much faster than x=A\b for large matrices. The algorithm will check to see if A is symmetric and use a more efficient algorithm if it is. Users are encouraged to improve and redistribute this script.

Acknowledgements

Fast Tridiagonal System Solver inspired this file.

MATLAB release MATLAB 6.0 (R12)
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Comments and Ratings (7)
09 Aug 2014 AAAA  
10 Dec 2013 jeon jiyeon

Good

08 Dec 2007 Tim Davis

For production use, this function is superseded by x=A\b in MATLAB, which now includes a test for banded matrices (and uses LAPACK). I compared it in MATLAB 7.5 with A=spdiags(rand(n,5),-2:2,n,n); A=A+A'+10*speye(n) which is symmetric and positive definite. This pentsolve function was from 20x to 230x slower than x=A\b, as n increased from 100 to 10,000. The slowdown is linear; that is, this function seems to behave like O(n^2) time (which is surprising since the code doesn't have an O(n^2) behavior in it). The same thing occurs with unsymmetric banded matrices.

The accuracy of this function is fine. Its purpose now on the File Exchange is now no longer the need for speed; it's only for illustrating an algorithm (for which it's still useful).

Thus, if you're looking just to solve Ax=b for your pentadiagonal system, just use x=A\b. If you want to read the code to understand an algorithm, then this code is still useful.

30 Jul 2007 Hassan R.

You can make slight changes to the code to fit your problem. You can save a lot of computation time.

14 Apr 2007 Mohd osman  
17 Aug 2004 Bastiaan Huisman

Great Stuff!

26 Apr 2004 Jagadeesha Kumar

Thanks a lot for this matlab code.. This has really made the execution of programs faster.. Thanks again...

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