Solving Linear Systems through Nested Dissection

Abstract--The generalized nested dissection method, developed by Lipton, Rose, and Tarjan, is a seminal method for solving a linear system Ax = b where A is a symmetric positive definite matrix. The method runs extremely fast whenever A is a well-separable matrix (such as matrices whose underlying support is planar or avoids a fixed minor). In this work we extend the nested dissection method to apply to any nonsingular well-separable matrix over any field. The running times we obtain essentially match those of the nested dissection method. Keywords-Gaussian elimination, linear system, nested dissection.

• Type: Journal
• Year: 2010
• Where: FOCS
• Authors: Noga Alon, Raphael Yuster
• Keywords: FOCS 2010, Generalized Nested Dissection, Nested Dissection Method, Theoretical Computer Science, Well-separable Matrix