Rate of convergence of discretization in Chebyshev approximation
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چکیده
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چکیده ندارد.
On Convergence and Degeneracy in Rational Padi and Chebyshev Approximation *
We study two questions associated with rational approximation of a function f(z) near the origin z-0: continuity of the Pad approximation operator, and convergence of Chebyshev to Pad ap-proximants as the domain of approximation shrinks to a point. Both become delicate in the case of degenerate approximations, i.e. approximations whose numerator and denominator are deficient in degree. In this ...
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The theorem proved here extends the author's previous work on Chebyshev series [4] by showing that if f(x) is a member of the class of so-called "Stieltjes functions" whose asymptotic power series 2 anx" about x = 0 is such that ttlogjaj _ hm —;-= r, «log n then the coefficients of the series of shifted Chebyshev polynomials on x e [0, a],2b„Tf(x/a), satisfy the inequality 2 . m log | (log |M) ...
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The discretization approach for solving semi-infinite optimization problems is considered. We are interested in the rate of the approximation error between the solution of the semi-infinite problem and the solution of the discretized program depending on the discretization mesh-size d. It will be shown how this rate depends on whether the minimizer is strict of order one or two and on whether t...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1981
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1981-0616366-x