Code covered by the BSD License

### Highlights from Fast Pentadiagonal System Solver

4.2
4.2 | 5 ratings Rate this file 15 Downloads (last 30 days) File Size: 2.01 KB File ID: #4671 Version: 1.0

### Greg von Winckel (view profile)

23 Mar 2004 (Updated )

Solves symmetric and asymmetric pentadiagonal systems.

File Information
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)
09 Aug 2014 AAAA

### AAAA (view profile)

10 Dec 2013 jeon jiyeon

### jeon jiyeon (view profile)

Good

Comment only
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For production use, this function is superseded by x=A\b in MATLAB, which now includes a test for banded matrices (and uses LAPACK).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.

Comment only
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!