This paper presents Levinson-type algorithms for (i) polynomial fitting, (ii) obtaining a Q decomposition of Vandermonde matrices and a Cholesky factorization of Hankel matrices and (iii) obtaining the inverse of Hankel matrices. The algorithm for the least-squares solution of Hankel systems of equations, requires 3n + 9n+ 3 multiply and divide operation (MD0). The algorithm for obtaining an or...

In this paper we derive a fast O(n) algorithm for solving linear systems where the coefficient matrix is a polynomial-Vandermonde VR(x) = [rj−1(xi)] matrix with polynomials R related to a quasiseparable matrix. The result is a generalization of the well-known Björck-Pereyra algorithm for classical Vandermonde systems. As will be shown, many important systems of polynomials are related to quasis...

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

In this paper we carry over the Björck-Pereyra algorithm for solving Vandermonde linear systems to what we suggest to call Szegö-Vandermonde systems VΦ(x), i.e., polynomialVandermonde systems where the corresponding polynomial system Φ is the Szegö polynomials. The properties of the corresponding unitary Hessenberg matrix allow us to derive a fast O(n2) computational procedure. We present numer...

We study combinations of many-sorted algebraic term rewriting systems and polymorphic lambda term rewriting. Algebraic and lambda terms are mixed by adding the symbols of the algebraic signature to the polymorphic lambda calculus, as higher-order constants. We show that if a many-sorted algebraic rewrite system R has the Church-Rosser property (is confluent), then R + β + type-β + type-η rewrit...

We define multidimensional Vandermonde matrices (MV) to be certain submatrices of Kronecker products of standard Vandermonde matrices. These MV matrices appear naturally in multidimensional problems of polynomial interpolation. An explicit algorithm is produced to solve systems of linear equations with MV matrices of coefficients. This is an extension of work of Stenger for the two-dimensional ...

Matrices with the structures of Toeplitz, Hankel, Vandermonde and Cauchy types are omnipresent in modern computations in Sciences, Engineering and Signal and Image Processing. The four matrix classes have distinct features, but in [P90] we showed that Vandermonde and Hankel multipliers transform all these structures into each other and proposed to employ this property in order to extend any suc...

An n-variate Vandermonde polynomial is the determinant of the n × n matrix where the ith column is the vector (1, xi, x 2 i , . . . , x n−1 i ) T . Vandermonde polynomials play a crucial role in the theory of alternating polynomials and occur in Lagrangian polynomial interpolation as well as in the theory of error correcting codes. In this work we study structural and computational aspects of l...

In this paper we rst show that a con uent Vandermonde matrix may be viewed as composed of some rows of a certain block Vandermonde matrix As a result we derive a Sylvester s structure for this class of matrices that ap pears as a natural generalization of the straightforward one known for usual Vandermonde matrices Then we present some applications as an illustration of the established structur...