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Higher order numerical differentiation on the Infinity Computer

Sergeyev, Yaroslav (2011) Higher order numerical differentiation on the Infinity Computer. Optimization Letters, 5 (4). pp. 575-585.

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Abstract

There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of information. In this paper, a new way to do this is presented for a new kind of a computer – the Infinity Computer – able to work numerically with finite, infinite, and infinitesimal numbers. It is proved that the Infinity Computer is able to calculate values of derivatives of a higher order for a wide class of functions represented by computer procedures. It is shown that the ability to compute derivatives of arbitrary order automatically and accurate to working precision is an intrinsic property of the Infinity Computer related to its way of functioning. Numerical examples illustrating the new concepts and numerical tools are given.


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Item Type: Published Article or Volume
Creators:
CreatorsEmailORCID
Sergeyev, Yaroslavyaro@dimes.unical.it0000-0002-1429-069X
Keywords: Higher order numerical differentiation, infinite and infinitesimal numbers, Infinity Computer
Subjects: Specific Sciences > Cognitive Science > Computation
Specific Sciences > Computation/Information
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Mathematics
Specific Sciences > Cognitive Science > Perception
Depositing User: Prof. Yaroslav Sergeyev
Date Deposited: 30 Sep 2024 21:08
Last Modified: 30 Sep 2024 21:08
Item ID: 23938
Journal or Publication Title: Optimization Letters
Publisher: Springer
Official URL: https://link.springer.com/article/10.1007/s11590-0...
DOI or Unique Handle: 10.1007/s11590-010-0221-y
Subjects: Specific Sciences > Cognitive Science > Computation
Specific Sciences > Computation/Information
Specific Sciences > Cognitive Science > Concepts and Representations
Specific Sciences > Mathematics
Specific Sciences > Cognitive Science > Perception
Date: 2011
Page Range: pp. 575-585
Volume: 5
Number: 4
URI: https://philsci-archive.pitt.edu/id/eprint/23938

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