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Effective approximation of piecewise smooth functions by their expansion into fast convergent series in terms of functions formed by eigenfunctions of Sturm-Liouville problems. (English) Zbl 1064.65076
The author proposes a method of constructing the specific functional bases of binary sets of eigenfunctions for the Sturm-Liouville operator of a general form.
MSC:
65L15 Numerical solution of eigenvalue problems involving ordinary differential equations
34L16 Numerical approximation of eigenvalues and of other parts of the spectrum of ordinary differential operators
34B24 Sturm-Liouville theory
41A30 Approximation by other special function classes
41A10 Approximation by polynomials
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