A Generalization of the Bernstein Polynomials
Copyright policy )A Generalization of the Bernstein Polynomials
The author generalizes the Bernstein polynomials by taking averages of point evaluations of the function \(f\) instead of the usual values \(f(i/n)\). The number of point evaluations \(s_n\) taken for the \(n\)th polynomial, may grow to \(\infty\) as \(n\to\infty\), but it is necessary and sufficient for insuring approximation of continuous functions, that \(s_n/n\to 0\). An estimate on the degree of approximation involving the modulus of continuity of \(f\) is also given.
- Fudan University China (People's Republic of)
Approximation by polynomials, Applied Mathematics, Approximation by positive operators, Rate of convergence, degree of approximation, degree of approximation, Bernstein polynomials, Analysis
Approximation by polynomials, Applied Mathematics, Approximation by positive operators, Rate of convergence, degree of approximation, degree of approximation, Bernstein polynomials, Analysis
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