Several representations for the interpolating polynomial exist: Lagrange, Newton, orthogonal polynomials etc. Each representation is characterized by some basis functions. In this paper we investigate the transformations between the basis functions which map a specific representation to another. We show that for this purpose the LU and the QR decomposition of the Vandermonde matrix play a cruci...

Efficient speech signal representations are prerequisite for efficient speech processing algorithms. The Vandermonde transform is a recently introduced time-frequency transform which provides a sparse and uncorrelated speech signal representation. In contrast, the Fourier transform only decorrelates the signal approximately. To achieve complete decorrelation, the Vandermonde transform is signal...

Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. In this paper, an effective algorithm is presented for computing the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton’s interpolation method with erro...

In [P90] we proposed to employ Vandermonde and Hankel multipliers to transform into each other the matrix structures of Toeplitz, Hankel, Vandermonde and Cauchy types as a means of extending any successful algorithm for the inversion of matrices having one of these structures to inverting the matrices with the structures of the three other types. Surprising power of this approach has been demon...

This paper is concerned with the generalized Euler polynomial matrix $\E^{(\alpha)}(x)$ and $\E$. Taking into account some properties of polynomials numbers, we deduce product formulae for determine inverse We establish explicit expressions $\E(x)$, which involving Pascal, Fibonacci Lucas matrices, respectively. From these get new interesting identities numbers. Also, provide factorizations in ...

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in O (̃α2n) operations, where n is the matrix size, α is its displacement rank, and O ̃ denotes the omission of logarithmic factors. We show that for such matrices, this cost can be reduced to O (̃αω−1n), where ω is a feasible exponent for matrix multiplication over the base field. The best known estimate...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 20 November 2019Accepted: 14 July 2020Published online: 06 May 2021Keywordsinterpolation, least-squares, Vandermonde matrix, Arnoldi, polyval, polyfit, Fourier extensionAMS Subject Headings41A05, 65D05, 65D10Publication DataISSN (print): 0036-1445ISSN (online): 1095-7200P...

Joshua J. Waterfall, Fergal P. Casey, Ryan N. Gutenkunst, Kevin S. Brown, Christopher R. Myers, Piet W. Brouwer, Veit Elser, James P. Sethna 1 Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY 14853, USA 2 Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA 3 Department of Molecular and Cellular Biology, Harvard University, Cambridge, MA 02138, U...

Modern speech codecs based on Code Excited Linear Prediction (CELP) employ an analysis-by-synthesis optimization loop to find the best quantization of the source model parameters. With this approach, optimal quantization can be achieved only with an exhaustive search. Instead, we propose to use matrix factorization to decorrelate the objective function of the optimization problem, whereby the c...