Verified Correctness, Accuracy, and Convergence of a Stationary Iterative Linear Solver: Jacobi Method

Mohit Tekriwal, Andrew W. Appel, Ariel E. Kellison, David Bindel, Jean-Baptiste Jeannin

Abstract: Solving a sparse linear system of the form \(Ax=b\) is a common engineering task, e.g., as a step in approximating solutions of differential equations. Inverting a large matrix A is often too expensive, and instead engineers rely on iterative methods, which progressively approximate the solution x of the linear system in several iterations, where each iteration is a much less expensive (sparse) matrix-vector multiplication.