Related papers: Solution of Interpolation Problems via the Hankel …
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
Estimating camera geometry typically involves solving minimal problems formulated as systems of multivariate polynomial equations, which often pose computational challenges when using existing Gr\"obner-basis or resultant-based methods due…
The nonlinear inverse problem of exponential data fitting is separable since the fitting function is a linear combination of parameterized exponential functions, thus allowing to solve for the linear coefficients separately from the…
In the paper Description of the $K$-spaces by means of $J$-spaces and the reverse problem, Math. Nachr. 296 (2023), no. 9, 4002--4031, we have establish conditions under which the limiting $K$-space $(X_0,X_1)_{0,q,b;K}$, involving a slowly…
For $m,n \in \mathbb{N}$, $m\geq 1$ and a given function $f : \mathbb{R}^m\longrightarrow \mathbb{R}$ the polynomial interpolation problem (PIP) is to determine a \emph{generic node set} $P \subseteq \mathbb{R}^m$ and the coefficients of…
Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…
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…
We reconsider the theory of Lagrange interpolation polynomials with multiple interpolation points and apply it to linear algebra. For instance, $A$ be a linear operator satisfying a degree $n$ polynomial equation $P(A)=0$. One can see that…
In this article, we prove the following interpolation problem: if the composition of a function and a regular map between affine varieties is a regular function, then there exists a global regular function of the target variety that…
The goal of this work is to introduce a local and a global interpolator in Jacobi-weighted spaces, with optimal order of approximation in the context of the $p$-version of finite element methods. Then, an a posteriori error indicator of the…
The quantitative estimation for the interpolation error constants of the Fujino-Morley interpolation operator is considered. To give concrete upper bounds for the constants, which is reduced to the problem of providing lower bounds for…
In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great…
We prove some interpolation inequalities which arise in the analysis of pattern formation in physics. They are the strong version of some already known estimates in weak form that are used to give a lower bound of the energy in many…
Fractal interpolation technique is an alternative to the classical interpolation methods especially when a chaotic signal is involved. The logic behind the formulation of an iterated function system for the construction of fractal…
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for…
In this paper, we consider methods to compute the coefficients of interpolants relative to a basis of polynomials satisfying a three-term recurrence relation. Two new algorithms are presented: the first constructs the coefficients of the…
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…
It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…
We describe geometrically and algebraically the set of unattainable points for the Rational Hermite Interpolation Problem (i.e. those points where the problem does not have a solution). We show that this set is a union of equidimensional…