Computational Physics Lectures: Linear Algebra methods

LU Decomposition, linear equations

The algorithm goes as follows

Set up the matrix \( \bf A \) and the vector \( \bf w \) with their correct dimensions. This determines the dimensionality of the unknown vector \( \bf x \).
Then LU decompose the matrix \( \bf A \) through a call to the function ludcmp(double a, int n, int indx, double &d). This functions returns the LU decomposed matrix \( \bf A \), its determinant and the vector indx which keeps track of the number of interchanges of rows. If the determinant is zero, the solution is malconditioned.
Thereafter you call the function lubksb(double a, int n, int indx, double w) which uses the LU decomposed matrix \( \bf A \) and the vector \( \bf w \) and returns \( \bf x \) in the same place as \( \bf w \). Upon exit the original content in \( \bf w \) is destroyed. If you wish to keep this information, you should make a backup of it in your calling function.