Matrix recursive interpolation algorithm for block linear systems: Direct methods Original Research Article

This paper presents an unified algorithm for solving systems of matrix and block linear equations. Solving a system of block linear equations will be interpreted as a matrix interpolation problem. This new approach gives us a general algorithm called the matrix recursive interpolation algorithm (MRIA), which includes block direct methods. The orthogonal version of the MRIA will be given and denoted by OMRIA. We will also show how to choose two free parameters in the MRIA for obtaining known and new block direct methods.