Volume 9, Issue 2
Tricks of the Trade
In and Out
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In and Out
Q: One can use LinearSolve to solve a system of linear equations. However, I work with very large matrices having only five nonzero diagonals. Are there efficient methods for dealing with such matrices?
A: Daniel Lichtblau (email@example.com) answers: If you require only machine arithmetic, this can be done effectively using the built-in sparse linear solver in Version 5. Here is an example.
Create a diagonally-dominant random sparse -diagonal matrix using SparseArray.
With and , we obtain a sparse array with nonzero elements.
Use Normal to obtain the ordinary array corresponding to a sparse array object.
Produce a pentadiagonal sparse matrix of dimension 2000.
Solve for a random right-hand side.
Compare with the time required for an ordinary (nonsparse) matrix.
Check that the solutions agree using (for matrices, gives the maximum singular value of ).
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