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Optimization of parameters in the Menzerath–Altmann law

Ján Andres, Lubomír Kubáček, Jitka Machalová, Michaela Tučková (2012)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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 c is investigated as well. Finally, the obtained results are discussed by means of an illustrative example from quantitative linguistics....

Quadratic splines smoothing the first derivatives

Jiří Kobza (1992)

Applications of Mathematics

The extremal property of quadratic splines interpolating the first derivatives is proved. Quadratic spline smoothing the given values of the first derivative, depending on the knot weights w i and smoothing parameter α , is then studied. The algorithm for computing appropriate parameters of such splines is given and the dependence on the smoothing parameter α is mentioned.

Reference points based recursive approximation

Martina Révayová, Csaba Török (2013)

Kybernetika

The paper studies polynomial approximation models with a new type of constraints that enable to get estimates with significant properties. Recently we enhanced a representation of polynomials based on three reference points. Here we propose a two-part cubic smoothing scheme that leverages this representation. The presence of these points in the model has several consequences. The most important one is the fact that by appropriate location of the reference points the resulting approximant of two...

Reference points based transformation and approximation

Csaba Török (2013)

Kybernetika

Interpolating and approximating polynomials have been living separately more than two centuries. Our aim is to propose a general parametric regression model that incorporates both interpolation and approximation. The paper introduces first a new r -point transformation that yields a function with a simpler geometrical structure than the original function. It uses r ≥ 2 reference points and decreases the polynomial degree by r - 1 . Then a general representation of polynomials is proposed based on r ≥ 1 reference...

Currently displaying 101 – 120 of 150