Cyclic reduction and FACR methods for piecewise Hermite bicubic orthogonal spline collocation (Q1344103)

The paper studies the solution of linear systems resulting from piecewise Hermite bicubic orthogonal spline collocation for separable partial differential equations on a rectangle. It is shown that cyclic reduction (CR) and Fourier analysis-cyclic reduction (FACR) methods can be applied. On an \(N\times N\) uniform grid these methods require \(O(N^ 2\log N)\) and \(O(N^ 2\log\log N)\) arithmetic operations, respectively.