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Difference operators from interpolating moving least squares and their deviation from optimality

Thomas Sonar (2005)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp. 37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.

Difference operators from interpolating moving least squares and their deviation from optimality

Thomas Sonar (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the classical Interpolating Moving Least Squares (IMLS) interpolant as defined by Lancaster and Šalkauskas [Math. Comp.37 (1981) 141–158] and compute the first and second derivative of this interpolant at the nodes of a given grid with the help of a basic lemma on Shepard interpolants. We compare the difference formulae with those defining optimal finite difference methods and discuss their deviation from optimality.

Direct solution of nonlinear constrained quadratic optimal control problems using B-spline functions

Yousef Edrisi Tabriz, Mehrdad Lakestani (2015)

Kybernetika

In this paper, a new numerical method for solving the nonlinear constrained optimal control with quadratic performance index is presented. The method is based upon B-spline functions. The properties of B-spline functions are presented. The operational matrix of derivative ( 𝐃 φ ) and integration matrix ( 𝐏 ) are introduced. These matrices are utilized to reduce the solution of nonlinear constrained quadratic optimal control to the solution of nonlinear programming one to which existing well-developed...

Discrete smoothing splines and digital filtration. Theory and applications

Jiří Hřebíček, František Šik, Vítězslav Veselý (1990)

Aplikace matematiky

Two universally applicable smoothing operations adjustable to meet the specific properties of the given smoothing problem are widely used: 1. Smoothing splines and 2. Smoothing digital convolution filters. The first operation is related to the data vector r = ( r 0 , . . . , r n - 1 ) T with respect to the operations 𝒜 , ℒ and to the smoothing parameter α . The resulting function is denoted by σ α ( t ) . The measured sample r is defined on an equally spaced mesh Δ = { t i = i h } i = 0 n - 1 ...

Dislocation dynamics - analytical description of the interaction force between dipolar loops

Vojtěch Minárik, Jan Kratochvíl (2007)

Kybernetika

The interaction between dislocation dipolar loops plays an important role in the computation of the dislocation dynamics. The analytical form of the interaction force between two loops derived in the present paper from Kroupa’s formula of the stress field generated by a single dipolar loop allows for faster computation.

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