Tridiagonal systems, and the evaluation of polynomials revisited [CRUNCH]

In the previous installment, we looked at some generalpurpose linear solvers???some approaches to solving systems of simultaneous linear algebraic equations for cases in which there are no distinctive features offered by the coefficient matrix used in the description of the system. We concentrated on Gaussian elimination and LU decomposition. The computational effort required to solve an n-square system via either of those techniques is O(n³), although, as was pointed out, solution via LU decomposition requires only O(n²) arithmetic operations after the factorization is complete. Thus, solving a system of linear equations for more than one right-hand side (i.e., for more than one forcing vector) enjoys significant computational economy when LU decomposition is employed instead of Gaussian elimination.