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The best uniform quadratic approximation of circular arcs with high accuracy

100%

Rababah A.

Open Mathematics

2016

tom 14

nr 1

118-127

In this article, the issue of the best uniform approximation of circular arcs with parametrically defined polynomial curves is considered. The best uniform approximation of degree 2 to a circular arc is given in explicit form. The approximation is constructed so that the error function is the Chebyshev polynomial of degree 4; the error function equioscillates five times; the approximation order is four. For θ = π/4 arcs (quarter of a circle), the uniform error is 5.5 × 10−3. The numerical examples demonstrate the efficiency and simplicity of the approximation method as well as satisfy the properties of the best uniform approximation and yield the highest possible accuracy.

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

100%

Efremova L., Freiling G.

Open Mathematics

2013

tom 11

nr 11

2044-2051

We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.

Ograniczanie wyników

2 Open Mathematics

1 Efremova L.

1 Freiling G.

1 Rababah A.

1 2016

1 2013

Wyniki wyszukiwania

The best uniform quadratic approximation of circular arcs with high accuracy

Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials