Hermite's formula for vector polynomial interpolation with applications to structured matrices

Abstract

The classical Hermite formula for polynomial interpolation is generalized to interpolation of vector polynomials (tangential interpolation). The formula exhibits a relation between the matricial homogeneous problem and the nonhomogeneous vector problem. As applications, a formula for the inverse of a generalized Vandermonde matrix is presented and it is shown that the well-known formulas for the inverse of a Toeplitz matrix can be obtained as a special case of the generalized Hermite formula.

Keywords:

• Hermite interpolation
• tangential interpolation
• Vandermonde matrix
• Toeplitz matrix

^*email: georg@math- 1 .sci.kuniv.edu.kw, musallam@math-1 .sci.kuniv.edu.kw

^*email: georg@math- 1 .sci.kuniv.edu.kw, musallam@math-1 .sci.kuniv.edu.kw

Notes

^*email: georg@math- 1 .sci.kuniv.edu.kw, musallam@math-1 .sci.kuniv.edu.kw