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Re: Solving Simultaneous Equations with Matrices

by tsee (Curate)
on Apr 28, 2004 at 15:08 UTC ( #348854=note: print w/ replies, xml ) Need Help??

in reply to Solving Simultaneous Equations with Matrices

Another alternative would be to use Math::Symbolic to solve certain classes of equations. The manual of Math::Symbolic::MiscAlgebra has the following on it:

linear_solve Calculates the solutions x (vector) of a linear equation system of the form "Ax = b" with "A" being a matrix, "b" a vector and the solution "x" a vector. Due to implementation limitations, "A" must be a quadratic matrix and "b" must have a dimension that is equivalent to that of "A". Furthermore, the determinant of "A" must be non-zero. The algorithm used is devised from Cramer's Rule and thus inefficient. The preferred algorithm for this task is Gaussian Elimination. If you have a matrix and a vector of real numbers, please consider using either Math::MatrixReal or Math::Pari instead.

Note that the complexity of Cramer's rule is O(n!) whereas Gaussian Elimination works in O(n^3) as noted by others in this thread.


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