Numerical residual elimination method of finite differential equations (Q1261523)

The authors consider the numerical solution of systems of linear equations with a strictly banded coefficient matrix \(A\) of band width \(m\) that arise from the discretization of linear one-dimensional boundary value problems. Under the assumption \(a_{i,m+i}\neq 0\) for \(i=1,2,\dots,n-m\) an algorithm is proposed that reduces the original problem to the solution of only \(m\) variational equations for the corrections of the \(m\) initially guessed first unknowns. Although the authors claim that the computed solution is exact (!), the process is likely to be unstable.