Solving Systems of Linear Equations

A square system of linear equations has the form Ax = b, where A is a user-specified n × n matrix, b is a given right-hand side n vector, and x is the solution n vector. Each entry of A and b must be specified. The entire vector x is returned as output.

When A is invertible, a unique solution to Ax = b exists. The most commonly used direct method for solving Ax = b factors the matrix A into a product of triangular matrices and solves the resulting triangular systems of linear equations. Functions that use direct methods for solving systems of linear equations all compute the solution to Ax = b. Thus, if function imsl.linalg.lu_solve() is called with the required arguments, x is returned by default.

To perform additional tasks, such as only factoring the matrix A into a product of triangular matrices, use the specific functions from the imsl.linalg package.