Matrix expression of hermite interpolation polynomials

Quantum Hermite Interpolation Polynomials

Abstract. The concept of Lagrange and Hermite interpolation polynomials can be generalized. The spectral basis of idempotents and nilpotents of a factor ring of polynomials provides a powerful framework for the expression of Lagrange and Hermite interpolation in 1, 2 and higher dimensional spaces. We give a new definition of quantum Lagrange and Hermite interpolation polynomials which works on ...

On Hermite-hermite Matrix Polynomials

In this paper the definition of Hermite-Hermite matrix polynomials is introduced starting from the Hermite matrix polynomials. An explicit representation, a matrix recurrence relation for the Hermite-Hermite matrix polynomials are given and differential equations satisfied by them is presented. A new expansion of the matrix exponential for a wide class of matrices in terms of Hermite-Hermite ma...

Hermite and Hermite-Fejér interpolation for Stieltjes polynomials

Let wλ(x) := (1−x2)λ−1/2 and P (λ) n be the ultraspherical polynomials with respect to wλ(x). Then we denote by E (λ) n+1 the Stieltjes polynomials with respect to wλ(x) satisfying ∫ 1 −1 wλ(x)P (λ) n (x)E (λ) n+1(x)x dx { = 0, 0 ≤ m < n+ 1, = 0, m = n+ 1. In this paper, we show uniform convergence of the Hermite–Fejér interpolation polynomials Hn+1[·] and H2n+1[·] based on the zeros of the Sti...

Erratum: On a Hermite interpolation by polynomials of two variables

Explicit Hermite Interpolation Polynomials via the Cycle Index with Applications

The cycle index polynomial of a symmetric group is a basic tool in combinatorics and especially in Pólya enumeration theory. It seems irrelevant to numerical analysis. Through Faá di Bruno’s formula, cycle index is connected with numerical analysis. In this work, the Hermite interpolation polynomial is explicitly expressed in terms of cycle index. Applications in Gauss-Turán quadrature formula ...