A commuting family of symmetric matrices are called the block Jacobi matrices, if they are block tridiagonal. They are related to multivariate orthogonal polynomials. We study their eigenvalues and joint eigenvectors. The joint eigenvalues of the truncated block Jacobi matrices correspond to the common zeros of the multivariate orthogonal polynomials.

As two-dimensional coupled system of nonlinear partial differential equations does not give enough smooth solutions, when approximated by linear, quadratic and cubic polynomials and gives poor convergence or no convergence. In such cases, approximation by zero degree polynomials like Haar wavelets (continuous functions with finite jumps) are most suitable and reliable. Therefore, modified numer...

summary by Philippe Dumas] Linear recurrences and linear diierential equations with polynomial coeecients provide a nite representation of special functions or special sequences. Many algorithms are at our disposal; some give a way to automate the computation of recurrences or diierential equations; some provide solutions to recurrences or diierential equations; and some give the asymptotic beh...

The Lie Algebra package LieMath written in the Mathematica language constructs the beamline map in a singleexponent Lie generator form. The algorithm (a BCH-based map concatenation) has been recently enhanced with Truncated Power Series Algebra (TPSA) techniques. The polynomials produced by the series expansion of the Hamiltonian are replaced with arrays of coefficients (derivative structures) ...

A novel technique for extrapolation of transient response using early-time and low-frequency data is proposed in this paper. An improved extrapolation scheme using approximate prolate series is presented to obtain a transient electromagnetic response. The approximate prolate series, which has an approximately band-limited and sub-domain nature, is a better choice for extrapolating the timedomai...

Master equations are common descriptions of mesoscopic systems. Analytical solutions to these equations can rarely be obtained. We here derive an analytical approximation of the time-dependent probability distribution of the master equation using orthogonal polynomials. The solution is given in two alternative formulations: a series with continuous and a series with discrete support, both of wh...

Orthogonal functions and polynomials have been used by many authors for solving various problems. The main idea of using orthogonal basis is that a problem reduces to solving a system of linear or nonlinear algebraic equations by truncated series of orthogonal basis functions for solution of problem and using the operational matrices. Here we use Legendre wavelets basis on interval [0, 1]. Some...