Recently, Kulikov [1] presented the idea of double quasi-consistency, which facilitates global error estimation and control, considerably. More precisely , a local error control implemented in such methods plays a part of global error control at the same time. However, Kulikov studied only Nordsieck formulas and proved that there exists no doubly quasi-consistent scheme among those methods. In ...

Let $0 \lt p q\leq \infty $ and $\alpha \in (0,\infty ]$. We give a characterization of quasi-Banach interpolation spaces for the couple $(L_p(0,\alpha ),L_q(0,\alpha ))$ in terms two monotonicity properties, extending known results which mainly de

Here we study further the multivariate quasi-interpolation of sigmoidal and hyperbolic tangent types neural network operators of one hidden layer. We derive multivariate Voronovskaya type asymptotic expansions for the error of approximation of these operators to the unit operator. RESUMEN Aquí estudiamos extensiones de la cuasi-interpolación multivariada de operadores de redes neuronales de tip...

We show how to construct a stable hierarchical basis for piecewise quadratic C continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we construct a stable quasi-interpolation scheme for our sp...

We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a quasi-linear time complexity for substantial families of examples, for which no such result was known before. Applications are given to notably addition of a...

For a given function, we consider a problem of minimizing the P1 interpolation error on a set of triangulations with a fixed number of triangles. The minimization problem is reformulated as a problem of generating a mesh which is quasi-uniform in a specially designed metric. For functions with indefinite Hessian, we show existence of a family of metrics with highly diverse properties. The famil...

We introduce a new algorithm for fitting a Catmull-Clark subdivision surface to a given shape within a prescribed tolerance, based on the method of quasi-interpolation. The fitting algorithm is fast, local and scalable since it does not require the solution of linear systems. Its convergence rate is optimal for regular meshes and our experiments show that it behaves very well for irregular mesh...

A discrete method of accuracy O(hm) is constructed and justi ed for a class of Fredholm integral equations of the second kind with kernels that may have weak diagonal and boundary singularities. The method is based on improving the boundary behaviour of the kernel with the help of a change of variables, and on the product integration using quasi-interpolation by smooth splines of order m.

The Kötter–Nielsen–Høholdt algorithm is a popular way to construct the bivariate interpolation polynomial in the Guruswami–Sudan decoding algorithm for Reed–Solomon codes. In this paper, we show how one can use Divide & Conquer techniques to provide an asymptotic speed-up of the algorithm, rendering its complexity quasi-linear in n. Several of our observations can also provide a practical speed...

We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a quasi-linear time complexity for substantial families of examples, for which no such result was known before. Applications are given to notably addition of a...