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Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem
Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem
We consider the analysis and numerical solution of a forward-backward boundary value problem. We provide some motivation, prove existence and uniqueness in a function class especially geared to the problem at hand, provide various energy estimates, prove a priori error estimates for the Galerkin method, and show the results of some numerical computations.
Orthogonal bipolynomials
Orthogonal grids on meander-like regions.
Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line.
Orthogonal Least Squares Fitting with Linear Manifolds.
Orthogonal polynomials and quadrature.
Orthogonal polynomials and the Lanczos method
Lanczos method for solving a system of linear equations is well known. It is derived from a generalization of the method of moments and one of its main interests is that it provides the exact answer in at most n steps where n is the dimension of the system. Lanczos method can be implemented via several recursive algorithms known as Orthodir, Orthomin, Orthores, Biconjugate gradient,... In this paper, we show that all these procedures can be explained within the framework of formal orthogonal polynomials....
Orthogonal polynomials on the semicircle