A general approach to multivariable recursive interpolation

Multivariable Interpolation Problems

Entropy and Multivariable Interpolation

We define a new notion of entropy for operators on Fock spaces and positive definite multi-Toeplitz kernels on free semigroups. This is studied in connection with factorization theorems for (multi-Toeplitz, multi-analytic, etc.) operators on Fock spaces. These results lead to entropy inequalities and entropy formulas for positive definite multi-Toeplitz kernels on free semigroups (resp. multi-T...

A recursive approach to detect multivariable conditional variance components and conditional random effects

A complex trait like crop yield is determined by its component traits. Multivariable conditional analysis in a general mixed linear model is helpful in dissecting the gene expression for the complex trait due to different effects, such as environment, genotype, and genotype× environment interaction. A recursive approach is presented for constructing a new randomvector that can be equivalently u...

A New Approach to Improved Multiquadric Quasi-Interpolation by Using General Hermite Interpolation

Abstract In this paper, a new approach to improve univariate multiquadric operators is surveyed. The presented scheme is obtained by using Hermite interpolating polynomials where the function is approximated by generalized LB quasi-interpolation operator. Error analysis shows that the convergence rate depends on the shape parameter c. Thus, our operators could provide the desired smoothness and...

Generalized Recursive Multivariate Interpolation

A generalized recursive interpolation technique for a set of linear functionals over a set of general univariate basis functions has been previously developed. This paper extends these results to restricted multivariate interpolation over a set of general multivariate basis functions. When the data array is a suitable configuration (e.g., an ^-dimensional simplex), minimal degree multivariate i...