The polynomial interpolation based on a uniform grid yields the well-known Runge phenomenon. The maximum pointwise error is unbounded for functions with complex roots in the Runge zone. In this work, we first investigate the Runge phenomenon with the finite precision operations. We first show that the maximum error is bounded due to round-off errors inherent to the finite precision operation. T...

Using a matrix of drop size distributions (DSDs), measured by a microscale array of disdrometers, a method of spatial and temporal DSD interpolation is presented. The goal of this interpolation technique is to estimate the DSD above the disdrometer array as a function of three spatial coordinates, time and drop diameter. This interpolation algorithm assumes simpliŽ ed drop dynamics, based on cl...

in this paper a new element for analysis of thin-walled structures is presented, and the effects of secondary shear stresses on longitudinal displacements are examined. since the interpolation functions are based on non-uniform torsional differential equations, the analysis of stiffness matrix is facilitated. therefore, its ability to produce accurate results with the least number of elements i...

In this paper, we present an improved channel matrix estimation algorithm for orthogonalfrequency-divisionmultiplexing downlink mobile communication systems using comb-type pilot. The channel matrix, which contains the channel frequency response and the coefficients of inter-sub-carrierinterference (ICI), is estimated using parametric multipath channel model. In the algorithm, we assume the del...

A broad range of linear and non-linear equalization and precoding algorithms for wideband massive multi-user (MU) multiple-input multiple-output (MIMO) wireless systems that rely on orthogonal frequencydivision multiplexing (OFDM) or single-carrier frequency-division multiple access (SC-FDMA) requires the computation of the Gram matrix for each active subcarrier, which results in excessively hi...

We consider the problem of generating a matrix transfer function with prescribed strict bistability, biproperness, and positivity properties from a sequence of positive definite sample values at points on the frequency axis. We show how this arises in problems from multi-input/multioutput control analysis and design. This is a matrix interpolation problem with additional conditions, both on the...

Recently, spatial data set for fine zone scale becomes more important in urban planning. However, social or economic activity data such as transportation or production output are often difficult to get in the fine zone scale, due to the difficulties in survey. Comparing to these data, demographic data obtained in national census is able to easily get, so then an area interpolation by a regressi...

Spectra and pseudospectra of matrix polynomials are of interest in geometric intersection problems, vibration problems, and analysis of dynamical systems. In this note we consider the effect of the choice of polynomial basis on the pseudospectrum and on the conditioning of the spectrum of regular matrix polynomials. In particular, we consider the direct use of the Lagrange basis on distinct int...

According to V.P.Potapov, a classical interpolation problem can be reformulated in terms of a so-called Fundamental Matrix Inequality (FMI). To show that every solution of the FMI satisfies the interpolation problem, we usualy have to transform the FMI in some special way. In this paper the number of of transformations of the FMI which come into play are motivated and demonstrated by simple, bu...

We investigated an interpolation algorithm for computing the MoorePenrose inverse of a given polynomial matrix, based on the LeverrierFaddeev method. Also, a method for estimating the degrees of polynomial matrices arising from the Leverrier-Faddeev algorithm is given as the improvement of the interpolation algorithm. Algorithms are implemented in the symbolic programming language MATHEMATICA, ...