Early Automatic Differentiation: The Ch’in-Horner Algorithm

Early Automatic Differentiation: The Ch’in-Horner Algorithm A method for numerical solution of polynomial equations appeared in the 1247 a.d. book The Nine Sections of Mathematics, by Ch’in Kiu-shao. This procedure was rediscovered independently by W. G. Horner [1773–1827] at the beginning of the 19th century. Since their algorithm produces values of Taylor coefficients of polynomials, it can be viewed as an early example of automatic differentiation. For polynomials, their method is shown to be computationally equivalent to automatic generation of Taylor coefficients as introduced by R. E. Moore in 1962 for use on digital computers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Early Automatic Differentiation: The Ch’in-Horner Algorithm

Loading next page...
 
/lp/springer_journal/early-automatic-differentiation-the-ch-in-horner-algorithm-Yr3M0jn0ck
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2007 by Springer Science + Business Media B.V.
Subject
Mathematics; Numeric Computing; Mathematical Modeling and Industrial Mathematics; Approximations and Expansions; Computational Mathematics and Numerical Analysis
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-006-9028-z
Publisher site
See Article on Publisher Site

Abstract

A method for numerical solution of polynomial equations appeared in the 1247 a.d. book The Nine Sections of Mathematics, by Ch’in Kiu-shao. This procedure was rediscovered independently by W. G. Horner [1773–1827] at the beginning of the 19th century. Since their algorithm produces values of Taylor coefficients of polynomials, it can be viewed as an early example of automatic differentiation. For polynomials, their method is shown to be computationally equivalent to automatic generation of Taylor coefficients as introduced by R. E. Moore in 1962 for use on digital computers.

Journal

Reliable ComputingSpringer Journals

Published: Dec 20, 2006

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off