Implementation of Matrix Decomposition for Solving Linear Systems Arising in Orthogonal Spline Collocation for Separable Elliptic Boundary Value Problems

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This project is concerned with the development of software implementing new matrix decomposition algorithms which have been formulated for solving the systems of linear algebraic equations arising when orthogonal spline collocation (that is, spline collocation at Gauss points) is applied to certain separable, second order, linear problems on rectangular regions. Two classes of algorithms will be examined. In the first, the approximate solution is a piecewise Hermite bicubic defined on a uniform mesh, while the second provides approximations of arbitrarily high order on nonuniform partitions. The new algorithms, which are modular and possess a great deal of natural parallelism, also have application in the solution of nonseparable boundary value problems, problems on general regions, and time dependent problems. The new software will be written in Fortran and developed for use on various shared memory machines.