In recent works, we have studied linear predictive models constrained by time-domain filters. In the present study, we will study the one-dimensional case in more detail. Firstly, we obtain root-exchange properties between the roots of an all-pole model and corresponding constraints. Secondly, using the root-exchange property we can construct a novel matrix decomposition A RA = I, where R is a ...

Estimates for the rank of AMNV − UA † MN and more general displacement of A † MN are presented,where AMN is the weighted pseudoinverse of a matrix A.The results are applied to the close-to-Toeplitz,close-to-Vandermonde and close-to-Cauchy matrices.We extend the results due to G. Heinig and F. Hellinger in 1994.

A fast and accurate algorithm for solving a Bernstein-Vandermonde linear system is presented. The algorithm is derived by using results related to the bidiagonal decomposition of the inverse of a totally positive matrix by means of Neville elimination. The use of explicit expressions for the determinants involved in the process serves to make the algorithm both fast and accurate.

For xed matricesM and N , the linear transformation A 7! A MAN is called a displacement of the matrix A. Displacements can simplify matrix equations, as well as matrices themselves. Four principles to solve matrix equations are identi ed: 1) a variety of displacements are needed, 2) we want to recover a matrix from its displacement, 3) changing M and N is natural when A is transposed or inverte...

We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class techniques for providing straggler and fault tolerance in area coded computing. Our contributions are as follows: 1)We construct new codes matrix multiplication that achieve same fault/straggler previously constructed MatDot Codes Polynomial Codes.2)We show condition number every m ×m...

We develop a noncommutative analogue of the spectral decomposition with the quasideterminant defined by I. Gelfand and V. Retakh. In this theory, by introducing a noncommutative Lagrange interpolating polynomial and combining a noncommutative CayleyHamilton’s theorem and an identity given by a Vandermonde-like quasideterminant, we can systematically calculate a function of a matrix even if it h...