Approximation of a function by solutions of an underdetermined nonhomogeneous heat equation (Q1961039)
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scientific article; zbMATH DE number 1389244
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation of a function by solutions of an underdetermined nonhomogeneous heat equation |
scientific article; zbMATH DE number 1389244 |
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Approximation of a function by solutions of an underdetermined nonhomogeneous heat equation (English)
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15 June 2000
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The author considers the best approximation in the \(L_2\) sense of a given function by solutions of an underdetermined nonhomogeneous heat equation. The author reduces this problem to a well-posed boundary value problem for a fourth-order partial differential equation. In a one-dimensional spatial case, the author solves this well-posed problem by means of the eigenfunction expansion. The best found approximation and partial sums of its eigenfunction expansion provide an enhanced approximation of any unknown temperature distribution.
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heat equation
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boundary value
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Fourier series
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eigenfunction
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