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Browsing by Author "Chen, Jih-Hsiang"

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    Gauss-type formulas for linear functionals
    Chen, Jih-Hsiang (Virginia Polytechnic Institute and State University, 1982)
    We give a method, by solving a nonlinear system of equations, for Gauss harmonic interpolation formulas which are useful for approximating, the solution of the Dirichlet problem. We also discuss approximations for integrals of the form I(f) = (1/2πi) ∫L (f(z)/(z-α)) dz. Our approximations shall be of the form Q(f) = Σk=1n Akf(τk). We characterize the nodes τ₁, τ₂, …, τn, to get the maximum precision for our formulas. Finally, we propose a general problem of approximating for linear functionals; our results need further development.