Conditionally positive functions andp-norm distance matrices

Interpolation of Scattered Data: Distance Matrices and Conditionally Positive Definite Functions

Among other things, we prove that multiquadric surface interpolation is always solvable, thereby settling a conjecture of R. Franke.

Norm estimates for inverses of Toeplitz distance matrices

j=1 yj φ(‖x − xj‖2), x ∈ R , where φ: [0,∞) → R is some given function, (yj) n 1 are real coefficients, and the centres (xj) n 1 are points in R. For a wide class of functions φ, it is known that the interpolation matrix A = (φ(‖xj − xk‖2)) n j,k=1 is invertible. Further, several recent papers have provided upper bounds on ‖A‖2, where the points (xj) n 1 satisfy the condition ‖xj − xk‖2 ≥ δ, j ...

Pointwise Estimates Formultivariate Interpolation Using Conditionally Positive Definite Functions

We seek pointwise error estimates for interpolants, on scattered data, constructed using a basis of conditionally positive deenite functions of order m, and polynomials of degree not exceeding m-1. Two diierent approaches to the analysis of such interpolation are considered. The former uses distributions and reproducing kernel ideas, whilst the latter is based on a Lagrange function approach. E...

Generalized Hermite Interpolation via Matrix-valued Conditionally Positive Definite Functions

In this paper, we consider a broad class of interpolation problems, for both scalarand vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation ...

A norm inequality for pairs of commuting positive semidefinite matrices