Approximation Methods by Polynomials and Power-Series

Defining Power Series and Polynomials in Mizar

Least Squares Approximation by One-Pass Methods with Piecewise Polynomials

We propose several one-pass methods for data fitting in which a piecewise polynomial is used as an approximating function. The polynomial pieces are calculated step-by-step by the method of least squares as the data is -----------,scaIIIIed umy-once-from the begimring La tIre end. To calculate the least squares fitting in each step, we use three classes of data, namely: the data in the current ...

Approximation by homogeneous polynomials

A new, elementary proof is given for the fact that on a centrally symmetric convex curve on the plane every continuous even function can be uniformly approximated by homogeneous polynomials. The theorem has been proven before by Benko and Kroó, and independently by Varjú using the theory of weighted potentials. In higher dimension the new method recaptures a theorem of Kroó and Szabados, which ...

Approximation by polynomials

1. Introduction 2. The Weierstrass approximation theorem 3. Estimates for the Bernstein polynomials 4. Weierstrass' original proof 5. The Stone–Weierstrass approximation theorem 6. Chebyshev's theorems 7. Approximation by polynomials and trigonometric polynomials 8. The nonexistence of a continuous linear projection 9. Approximation of functions of higher regularity 10. Inverse theorems Referen...

Approximation By Trigonometric Polynomials

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