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# Algebraic Interpolation

• I. P. Mysovskih
Chapter
• 250 Downloads

## Abstract

Many numerical methods are based on the idea of replacing the functions which appear in the formulation of the problem by simpler functions which are close to the given ones in some sense. For example, to solve the equation φ(x) = 0 by Newton’s method, in the neighborhood of the initial approximation xo to the solution, the function φ(x) is replaced by the linear function
$${{\phi }_{0}}\left( x \right)\equiv \phi \left( {{x}_{0}} \right)+{\phi }'\left( {{x}_{0}} \right)\left( x-{{x}_{0}} \right).$$
The solution of the equation φ0(x) = 0 is taken as the next approximation to the solution of the equation φ(x) =0.

## Keywords

Finite Difference Decimal Place Remainder Term Divided Difference Hermite Interpolation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Copyright information

© Wolters-Noordhoff Publishing Groningen, The Netherlands 1969

## Authors and Affiliations

• I. P. Mysovskih
• 1
1. 1.Leningrad State UniversityRussia