Related papers: Subresultants, Sylvester sums and the rational int…
In this paper, we first apply the Fitzpatrick algorithm to osculatory rational interpolation. Then based on Fitzpatrick algorithm, we present a Neville-like algorithm for Cauchy interpolation. With this algorithm, we can determine the value…
We generalize Sylvester single sums to multisets (sets with repeated elements), and show that these sums compute subresultants of two univariate polyomials as a function of their roots independently of their multiplicity structure. This is…
We present a new formula for the Cauchy index of a rational function on an interval using subresultant polynomials. There is no condition on the endpoints of the interval and the formula also involves in some cases less subresultant…
In the space of all entire functions it is solved the problem of interpolation taking into account multiplicities by sums of the series of exponentials with the exponents from a given set. It is found a criterion of solubility of the…
This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…
We develop the convergence theory for a well-known method for the interpolation of functions on the real axis with rational functions. Precise new error estimates for the interpolant are de- rived using existing theory for trigonometric…
The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are…
Analytic interpolation problems with rationality and derivative constraints occur in many applications in systems and control. In this paper we present a new method for the multivariable case, which generalizes our previous results on the…
We consider interpolation of univariate functions on arbitrary sets of nodes by Gaussian radial basis functions or by exponential functions. We derive closed-form expressions for the interpolation error based on the…
Using algebraic methods, and motivated by the one variable case, we study a multipoint interpolation problem in the setting of several complex variables. The duality realized by the residue generator associated with an underlying Gorenstein…
We study regularity and decay properties for the solutions of the Cauchy problem for time-fractional partial differential equations, with tempered initial data, belonging to suitable (weighted) Sobolev spaces, associated with a differential…
A nonstandard application of bivariate polynomial interpolation is discussed: the implicitization of a rational algebraic curve given by its parametric equations. Three different approaches using the same interpolation space are considered,…
For finite dimensional CMV matrices the mixed inverse spectral problem of reconstruction the matrix by its submatrix and a part of its spectrum is considered. A general rational interpolation problem which arises in solving the mixed…
We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly…
We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the…
Multipoint polynomial evaluation and interpolation are fundamental for modern symbolic and numerical computing. The known algorithms solve both problems over any field of constants in nearly linear arithmetic time, but the cost grows to…
We present a new formula for the Hermite multivariate interpolation problem in the framework of the Chung--Yao approach. By using the respective univariate interpolation formula, we obtain a direct and explicit solution to the classical…
We present two new methods for multivariate exponential analysis. In [7], we developed a new algorithm for reconstruction of univariate exponential sums by exploiting the rational structure of their Fourier coefficients and reconstructing…
This paper presents a regularization technique for the high order efficient numerical evaluation of nearly singular, principal-value, and finite-part Cauchy-type integral operators. By relying on the Cauchy formula, the Cauchy-Goursat…
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…