Norms, Rounding Errors, Partial Derivatives and Fast Automatic Differentiation

Masao IRI; Koichi KUBOTA

Norms, Rounding Errors, Partial Derivatives and Fast Automatic Differentiation

Masao IRI, Koichi KUBOTA

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There are a number of problems in numerical computation which are of fundamental importance but for which no practicable method has been known. In this paper, problems concerning the norm, the rounding error and the partial differentiation are taken up, and what difficulties they have and why those difficulties have long been standing will be explained. Then, it will be shown that the method of "Fast Automatic Differentiation" which is attracting keen interest of those who are concerned will resolve all those difficulties through an effective method for partial differentiation. There, the concept of "computational graph" plays an important rôle. The relation to interval analysis will also be discussed from the point of view of assuring the quality of results of numerical computation.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E74-A No.3 pp.463-471

Publication Date: 1991/03/25

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Masao IRI
Koichi KUBOTA

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Masao IRI, Koichi KUBOTA, "Norms, Rounding Errors, Partial Derivatives and Fast Automatic Differentiation" in IEICE TRANSACTIONS on Fundamentals, vol. E74-A, no. 3, pp. 463-471, March 1991, doi: .
Abstract: There are a number of problems in numerical computation which are of fundamental importance but for which no practicable method has been known. In this paper, problems concerning the norm, the rounding error and the partial differentiation are taken up, and what difficulties they have and why those difficulties have long been standing will be explained. Then, it will be shown that the method of "Fast Automatic Differentiation" which is attracting keen interest of those who are concerned will resolve all those difficulties through an effective method for partial differentiation. There, the concept of "computational graph" plays an important rôle. The relation to interval analysis will also be discussed from the point of view of assuring the quality of results of numerical computation.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e74-a_3_463/_p

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@ARTICLE{e74-a_3_463,
author={Masao IRI, Koichi KUBOTA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Norms, Rounding Errors, Partial Derivatives and Fast Automatic Differentiation},
year={1991},
volume={E74-A},
number={3},
pages={463-471},
abstract={There are a number of problems in numerical computation which are of fundamental importance but for which no practicable method has been known. In this paper, problems concerning the norm, the rounding error and the partial differentiation are taken up, and what difficulties they have and why those difficulties have long been standing will be explained. Then, it will be shown that the method of "Fast Automatic Differentiation" which is attracting keen interest of those who are concerned will resolve all those difficulties through an effective method for partial differentiation. There, the concept of "computational graph" plays an important rôle. The relation to interval analysis will also be discussed from the point of view of assuring the quality of results of numerical computation.},
keywords={},
doi={},
ISSN={},
month={March},}

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TY - JOUR
TI - Norms, Rounding Errors, Partial Derivatives and Fast Automatic Differentiation
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 463
EP - 471
AU - Masao IRI
AU - Koichi KUBOTA
PY - 1991
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E74-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1991
AB - There are a number of problems in numerical computation which are of fundamental importance but for which no practicable method has been known. In this paper, problems concerning the norm, the rounding error and the partial differentiation are taken up, and what difficulties they have and why those difficulties have long been standing will be explained. Then, it will be shown that the method of "Fast Automatic Differentiation" which is attracting keen interest of those who are concerned will resolve all those difficulties through an effective method for partial differentiation. There, the concept of "computational graph" plays an important rôle. The relation to interval analysis will also be discussed from the point of view of assuring the quality of results of numerical computation.
ER -