A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles

A fast Schur complement algorithm is presented for computing the piecewise Hermite bicubic orthogonal spline collocation solution of the biharmonic Dirichlet problem on a rectangular region. On an N×N uniform partition, the algorithm, which involves the preconditioned conjugate gradient method and fast Fourier transforms, requires O(N2log2N) arithmetic operations.