Let x 0 , x 1 , . . ., x n ∈ ℝ, be pairwise disjoint, and let θ 0 , θ 1 , . . ., θ n ∈ Set θ := Σ ν=0 n θ ν . For each pair j, p such that 0 ≤ j ≤ n and 0 ≤ p ≤ θ j -1, let y j,p be a complex number. Then there is a unique polynomial, H(x), of degree θ - 1, such that H (p) (x j ) = y j,p , for 0 ≤ p ≤ θ j - 1, 0 ≤ j ≤ n. In particular, there is a unique fundamental Hermite polynomial, T j,p (x), of degree θ - 1, such that T j,p (r) (x s ) = δ j,s δ p,r , 0 ≤ r ≤ θ s - 1, 0 ≤ s ≤ n, δ being Kronecker's delta, and we have the representation. We give an explicit representation of the polynomials T j,p (x).
|Number of pages||7|
|Journal||Jaen Journal on Approximation|
|State||Published - 1 Dec 2018|
- Explicit representation of the fundamental polynomials
- Hermite interpolation