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) ∫<sub>L</sub> (f(z)/(z-α)) dz.
Our approximations shall be of the form
Q(f) = Σ<sub>k=1</sub><sup>n</sup> A<sub>k</sub>f(τ<sub>k</sub>).
We characterize the nodes τ₁, τ₂, …, τ<sub>n</sub>, to get the maximum precision for our formulas.
Finally, we propose a general problem of approximating for linear functionals; our results need further development. / Ph. D.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/74845 |
| Date | January 1982 |
| Creators | Chen, Jih-Hsiang |
| Contributors | Mathematics |
| Publisher | Virginia Polytechnic Institute and State University |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation, Text |
| Format | iv, 61, [1] leaves, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 9185708 |
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