# Finding All Solutions of Nonlinear Equations Using Linear Combinations of Functions

Finding All Solutions of Nonlinear Equations Using Linear Combinations of Functions As a computational method to find all solutions of nonlinear equations, interval analysis is well-known. In order to improve the computational efficiency of interval analysis, it is necessary to develop a powerful test for nonexistence of a solution in a given region. In this paper, a new nonexistence test is proposed which is more powerful than the conventional test. The basic idea proposed here is to apply the conventional test to linear combinations of functions. Effective linear combinations are proposed which make the nonexistence test very powerful. Using the proposed techniques, all solutions of nonlinear equations (including a system of 100 nonlinear equations and a system with strong nonlinearity which describes a transistor circuit) could be found very efficiently. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Finding All Solutions of Nonlinear Equations Using Linear Combinations of Functions

, Volume 6 (2) – Oct 7, 2004
10 pages

/lp/springer_journal/finding-all-solutions-of-nonlinear-equations-using-linear-combinations-DpRHS6h2Kk
Publisher
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009956920204
Publisher site
See Article on Publisher Site

### Abstract

As a computational method to find all solutions of nonlinear equations, interval analysis is well-known. In order to improve the computational efficiency of interval analysis, it is necessary to develop a powerful test for nonexistence of a solution in a given region. In this paper, a new nonexistence test is proposed which is more powerful than the conventional test. The basic idea proposed here is to apply the conventional test to linear combinations of functions. Effective linear combinations are proposed which make the nonexistence test very powerful. Using the proposed techniques, all solutions of nonlinear equations (including a system of 100 nonlinear equations and a system with strong nonlinearity which describes a transistor circuit) could be found very efficiently.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 7, 2004

## 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
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### 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.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations