arXiv subjects

Scott Kersey

Publications and source records attributed to Scott Kersey.

2 recordsLinked to original sources

arXiv2017

Rank of Submatrices of the Pascal Matrix

In a previous paper, we derived necessary and sufficient conditions for the invertibility of square submatrices of the Pascal upper triangular matrix. To do so, we established a connection with the two-point Birkhoff interpolation problem. In this paper, we extend this result by deriving a formula for the rank of submatrices of the Pascal matrix. Our formula works for both square and non-square submatrices. We also provide bases for the row and column spaces of these submatrices. Further, we apply our result to one-point lacunary polynomial approximation.

math.CO↗

arXiv2016

Discrete Polynomial Blending

In this paper we study "discrete polynomial blending," a term used to define a certain discretized version of curve blending whereby one approximates from the "sum of tensor product polynomial spaces" over certain grids. Our strategy is to combine the theory of Boolean Sum methods with dual bases connected to the Bernstein basis to construct a new quasi-interpolant for discrete blending. Our blended element has geometric properties similar to that of the Bernstein-B\'ezier tensor product surface patch, and rates of approximation that are comparable with those obtained in tensor product polynomial approximation.

math.NA↗