Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Directions for computing truncated multivariate Taylor series
HTML articles powered by AMS MathViewer

by Richard D. Neidinger PDF
Math. Comp. 74 (2005), 321-340 Request permission


Efficient recurrence relations for computing arbitrary-order Taylor coefficients for any univariate function can be directly applied to a function of $n$ variables by fixing a direction in $\mathbb {R}^{n}$. After a sequence of directions, the multivariate Taylor coefficients or partial derivatives can be reconstructed or “interpolated”. The sequence of univariate calculations is more efficient than multivariate methods, although previous work indicates a space cost for this savings and significant cost for the reconstruction. We completely eliminate this space cost and develop a much more efficient algorithm to perform the reconstruction. By appropriate choice of directions, the reconstruction reduces to a sequence of Lagrange polynomial interpolation problems in $\mathbb {R}^{n-1}$ for which a divided difference algorithm computes the coefficients of a Newton form. Another algorithm collects like terms from the Newton form and returns the desired multivariate coefficients.
Similar Articles
Additional Information
  • Richard D. Neidinger
  • Affiliation: Department of Mathematics, Davidson College, Box 7002, Davidson, North Carolina 28035
  • Email:
  • Received by editor(s): May 28, 2002
  • Received by editor(s) in revised form: June 10, 2003
  • Published electronically: May 17, 2004
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 321-340
  • MSC (2000): Primary 65D25, 65D05, 41A05, 41A63, 65Y20
  • DOI:
  • MathSciNet review: 2085414