# Numerical Analysis and Scientific Computing Seminar

## Euler-Maclaurin, Gregory, and Other Equally Spaced Interpolants

**Speaker:**
Nick Trefethen, Oxford and CIMS

**Location:**
Warren Weaver Hall 1302

**Date:**
Sept. 18, 2015, 10 a.m.

**Synopsis:**

Gauss quadrature amounts to integration of a polynomial interpolant in Legendre points, and the periodic trapezoidal rule to integration of a trigonometric interpolant in equispaced points. What about the Euler-Maclaurin formula, and its fully-discrete cousin the Gregory formula, for nonperiodic data in equispaced points? We show that these formulas too can be interpreted as integrals of interpolants. Then we consider more broadly the theory and practice of interpolation of smooth nonpriodic functions in equispaced points.