Related papers: About Nodal systems for Lagrange interpolation on …
We give several descriptions of positive quadrature formulas which are exact for trigonometric -, respectively, Laurent polynomials of degree less or equal $n-1-m$, $0\leq m\leq n-1$. A complete and simple description is obtained with the…
We first give a method to get multidimensional Leja sequences by considering intertwining sequences from one-dimensional ones. An application is the existence of explicit Leja sequences for the closed unit polydisc. Next, we deal with some…
We study the interpolation group whose elements are suitable pairs of formal power series. This group has a faithful representation into infinite lower triangular matrices and carries thus a natural structure as a Lie group. The matrix…
In this paper, the inverse spectral problem is applied to the integration of a periodic Volterra chain. A generalization of the Lagrange interpolation formula has been made.
Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these…
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
Some variants of the numerical Picard iterations method are presented to solve an IVP for an ordinary differential system. The term numerical emphasizes that a numerical solution is computed. The method consists in replacing the right hand…
We study the orbits of a polynomial f in C[X], namely the sets {e,f(e),f(f(e)),...} with e in C. We prove that if nonlinear complex polynomials f and g have orbits with infinite intersection, then f and g have a common iterate. More…
We present the abstract framework and some applications of interpolation theory. The main new result concerns interpolation between H^1 and L^p estimates for analytic families of operators acting on Schwartz functions.
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…
The maximum volume principle is investigated as a means to solve the following problem: Given a set of arbitrary interpolation nodes, how to choose a set of polynomial basis functions for which the Lagrange interpolation problem is…
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…
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…
A discrete Fourier analysis on the dodecahedron is studied, from which results on a tetrahedron is deduced by invariance. The results include Fourier analysis in trigonometric functions, interpolation and cubature formulas on these domains.…
The connection between continued fractions and orthogonality which is familiar for $J$-fractions and $T$-fractions is extended to what we call $R$-fractions of type I and II. These continued fractions are associated with recurrence…
A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in the study of the systems: the homogeneous potentials of…
This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation.…
A new alternative numerical procedure to the Szeg\H{o} quadrature formulas for the estimation of integrals with respect to a positive Borel measure $\mu$ supported on the unit circle is presented. As in many practical situations, we assume…
We refine the combinatorial 1-cocycle $\mathbb{L}R_{reg}$ for regular isotopies of long knots to a 1-cocycle with values in the free $\mathbb{Z}[x,x^{-1}]$-module generated by regular isotopy classes of oriented tangles with exactly one…
We consider how some methods of uniform and nonuniform interpolation by translates of radial basis functions -- specifically the so-called general multiquadrics -- perform in the presence of certain types of noise. These techniques provide…