نتایج جستجو برای: confluent vandermonde type systems

تعداد نتایج: 2422853  

Journal: :CoRR 2014
Sirani M. Perera Grigory Bonik Vadim Olshevsky

The results on Vandermonde-like matrices were introduced as a generalization of polynomial Vandermonde matrices, and the displacement structure of these matrices was used to derive an inversion formula. In this paper we first present a fast Gaussian elimination algorithm for the polynomial Vandermonde-like matrices. Later we use the said algorithm to derive fast inversion algorithms for quasise...

2008
Oyvind Ryan Merouane Debbah

Analytical methods for finding moments of random Vandermonde matrices with entries on the unit circle are developed. Vandermonde Matrices play an important role in signal processing and wireless applications such as direction of arrival estimation, precoding, and sparse sampling theory, just to name a few. Within this framework, we extend classical freeness results on random matrices with indep...

Journal: :Applied Mathematics and Computation 2005
Alfredo Eisinberg Giuseppe Fedele

This paper deals with Vandermonde matrices Vn whose nodes are the Gauss–Lobatto Chebyshev nodes, also called extrema Chebyshev nodes. We give an analytic factorization and explicit formula for the entries of their inverse, and explore its computational issues. We also give asymptotic estimates of the Frobenius norm of both Vn and its inverse and present an explicit formula for the determinant o...

2012
Walter Gautschi

Many problems in applied and numerical analysis eventually boil down to solving large systems of linear algebraic equations. Since the matrices and right-hand sides of such systems are typically the result of (sometimes extensive) computations, they are subject to an unavoidable level of noise caused by the rounding errors committed during their generation. It is then a matter of practical conc...

Journal: :Journal of Computational and Applied Mathematics 2023

We present a method to derive new explicit expressions for bidiagonal decompositions of Vandermonde and related matrices such as the (q-, h-) Bernstein-Vandermonde ones, among others. These results generalize existing nonsingular arbitrary rank. For totally nonnegative above classes, can be computed efficiently high relative accuracy componentwise in floating point arithmetic. In turn, matrix c...

2015
André Pierro de Camargo Stefano De Marchi

In the recent paper “On certain Vandermonde determinants whose variables separate” [Linear Algebra and its Applications 449 (2014) pp. 17–27], there was established a factorized formula for some bivariate Vandermonde determinants (associated to almost square grids) whose basis functions are formed by Hadamard products of some univariate polynomials. That formula was crucial for proving a conjec...

2013
Victor Y. Pan

Multipoint polynomial evaluation and interpolation are fundamental for modern algebraic and numerical computing. The known algorithms solve both problems over any field by using O(N log N) arithmetic operations for the input of size N , but the cost grows to quadratic for numerical solution. Our study results in numerically stable algorithms that use O(uN log N) arithmetic time for approximate ...

2016
Youness Aliyari Ghassabeh

Abstract: The inverse of a Vandermonde matrix has been used for signal processing, polynomial interpolation, curve fitting, wireless communication, and system identification. In this paper, we propose a novel fast recursive algorithm to compute the inverse of a Vandermonde matrix. The algorithm computes the inverse of a higher order Vandermonde matrix using the available lower order inverse mat...

2014
Christian Fischer Pedersen Tomas Bäckström

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...

Journal: :SIAM Journal on Applied Mathematics 2013

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