Optimale Quadraturformeln mit semidefiniten Kernen.
Optimale Quadraturformeln mit semidefiniten Peano-Kernen. - Optimal Integration Formulas with Semidefinite Peano-Kernels.
Optimality-preserving elimination of linearities in Jacobian accumulation.
Optimal-order quadratic interpolation in vertices of unstructured triangulations
We study the problem of Lagrange interpolation of functions of two variables by quadratic polynomials under the condition that nodes of interpolation are vertices of a triangulation. For an extensive class of triangulations we prove that every inner vertex belongs to a local six-tuple of vertices which, used as nodes of interpolation, have the following property: For every smooth function there exists a unique quadratic Lagrange interpolation polynomial and the related local interpolation error...
Optimization of parameters in the Menzerath–Altmann law
Four formulas of the Menzerath–Altmann law are tested from the point of view of their applicability and suitability. The accuracy of related approximations of measured data is examined by the least square method at first. Then the accuracy of calculated parameters in the formulas under consideration is compared statistically. The influence of neglecting parameter is investigated as well. Finally, the obtained results are discussed by means of an illustrative example from quantitative linguistics....
Optimization of Rational Approximations by Continued Fractions
The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.To get guaranteed machine enclosures of a special function f(x), an upper bound ε(f) of the relative error is needed, where ε(f) itself depends on the error bounds ε(app); ε(eval) of the approximation and evaluation error respectively. The approximation function g(x) ≈ f(x) is a rational function (Remez algorithm), and with sufficiently high polynomial degrees ε(app) becomes...
Optimization of the Raster-Scan Circle-Drawing Algorithm Based on Predicate Transformers
Orthogonal grids on meander-like regions.
Orthogonal Laurent polynomials and quadratures on the unit circle and the real half-line.
Orthogonal Least Squares Fitting with Linear Manifolds.
Orthogonal polynomials and quadrature.
Orthogonal polynomials on the semicircle
Orthonormal polynomial vectors and least squares approximation for a discrete inner product.
Oscillation Matrices with Spline Smoothing.