Interpolation

by J. F. Steffensen

Overview

In the mathematical subfield of numerical analysis, interpolation is a procedure that assists in "reading between the lines" in a set of tables by constructing new data points from existing points. This rigorous presentation employs only formulas for which it is possible to calculate error limits. Subjects include displacement symbols and differences, divided differences, formulas of interpolation, factorial coefficients, numerical differentiation, and construction of tables. Additional topics include inverse interpolation, elementary methods of summation, repeated summation, mechanical quadrature, numerical integration of differential equations, the calculus of symbols, interpolation with several variables, and mechanical cubature. 1950 edition.

Product Details

ISBN-13:	9780486450094
Publisher:	Dover Publications
Publication date:	03/17/2006
Series:	Dover Books on Mathematics Series
Edition description:	2nd ed.
Pages:	256
Product dimensions:	5.40(w) x 8.60(h) x 0.60(d)

Table of Contents

1. Introduction
2. Displacement-Symbols and Differences
3. Divided Differences
4. Interpolation-Formulas
5. Some Applications
6. Factorial Coefficients
7. Numerical Differentiation
8. Construction of Tables
9. Inverse Interpolation
10. Elementary Methods of Summation
11. Repeated Summation
12. Laplace's and Gauss’s Summation-Formulas
13. Bernoulli's Polynomials
14. Euler's Summation-Formula
15. Lubbock's and Woolhouse's Formulas
16. Mechanical Quadrature
17. Numerical Integration of Differential Equations
18. The Calculus of Symbols
19. Interpolation with Several Variables
20. Mechanical Cubature
Appendix