it has been proved that natural frequencies are stationary at the natural modes. also it has been shown that at the first mode it is a minimum and for systems with finite number of degrees of freedom the highest frequency is maximum (reference 1 and 2). beyond these statements nothing more can be said about the behavior of the natural frequencies without defining precisely the manner in which t...

An efficient implementation technique for the Lagrange interpolation is derived. This formulation called the Farrow structure leads to a version of Lagrange interpolation that is well suited to time varying FD filtering. Lagrange interpolation is mostly used for fractional delay approximation as it can be used for increasing the sampling rate of signals and systems. Lagrange interpolation is on...

In 1977 Chung and Yao introduced a geometric characterization in multivariate interpolation in order to identify distributions of points such that the Lagrange functions are products of real polynomials of first degree. We discuss and describe completely all these configurations up to degree 4 in the bivariate case. The number of lines containing more nodes than the degree is used for classifyi...

This text discusses barycentric Lagrange interpolation based on the SIAM REVIEW article of Jean-Paul Berrut and Lloyd N. Trefethen [1]. It also offers additional background information, as well as some MATLAB demonstrations. Interpolation Given a set Dn of n + 1 nodes x j with corresponding values f j where j = 0, . . . ,n, we aim to construct the polynomial that satisfies p(x j) = f j j = 0, ....

Abstract. We consider the finite element approximation of the Laplacian operator with the homogeneous Dirichlet boundary condition, and study the corresponding Lagrange interpolation in the context of finite element superconvergence. For ddimensional Qk-type elements with d ≥ 1 and k ≥ 1, we prove that the interpolation points must be the Lobatto points if the Lagrange interpolation and the fin...

We introduce and discuss a new computational model for Hermite–Lagrange interpolation by nonlinear classes of polynomial interpolants. We distinguish between an interpolation problem and an algorithm that solves it. Our model includes also coalescence phenomena and captures a large variety of known Lagrange-Hermite interpolation problems and algorithms. Like in traditional Hermite–Lagrange inte...

Introduction: To estimate the accuracy levels of Lagrange, Newton backward interpolation, and linear interpolation methods in estimating the output factors for square fields used in linear accelerator for 6 MV photons at various depths. Materials and Methods: Ionization measurements were carried out in radiation field analyzer in linear accelerator for 6 MV beams at the depths of 5 and 10 cm by...