Scientific Computing

This module illustrates LU factorization of a matrix using Gaussian elimination with pivoting. The initial matrix is reduced to upper triangular form by applying a sequence of elementary elimination matrices to annihilate the subdiagonal entries in successive columns. Each elementary elimination matrix is composed of an identity matrix plus some multipliers below the diagonal in the relevant column. Row interchanges (pivoting) can be used to avoid potential division by zero and limit the magnitudes of the multipliers, thereby enhancing numerical stability.

The user first selects a matrix size *n* = 2,** L** and

**Reference** Michael T. Heath,
*Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 2.4.4, especially Algorithm 2.4 and Example 2.16.

**Developers:** Jessica Schoen and Michael Heath