Abstract
A linear programming-based method is presented for finding all solutions of nonlinear systems of equations with guaranteed accuracy. In this method, a new effective linear programming-based method is used to delete regions in which solutions do not exist. On the other hand, Krawczyk's method is used to find regions in which solutions exist. As an illustrative example, all solutions of the nonlinear system of equations describing equilibrium conditions of the "high polymer liquid system", which is a well-known ill-conditioned system of equations, are identified by the method.
| Original language | English |
|---|---|
| Pages (from-to) | 171-177 |
| Number of pages | 7 |
| Journal | Journal of Universal Computer Science |
| Volume | 4 |
| Issue number | 2 |
| Publication status | Published - 1998 |
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Keywords
- All Solutions
- Guaranteed Accuracy
- Krawczyk's Method
- Linear Programming
- Nonlinear Equations
ASJC Scopus subject areas
- Computer Science(all)
Cite this
Finding all solutions of nonlinear systems of equations using linear programming with guaranteed accuracy. / Nakaya, Yusuke; Oishi, Shinichi.
In: Journal of Universal Computer Science, Vol. 4, No. 2, 1998, p. 171-177.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Finding all solutions of nonlinear systems of equations using linear programming with guaranteed accuracy
AU - Nakaya, Yusuke
AU - Oishi, Shinichi
PY - 1998
Y1 - 1998
N2 - A linear programming-based method is presented for finding all solutions of nonlinear systems of equations with guaranteed accuracy. In this method, a new effective linear programming-based method is used to delete regions in which solutions do not exist. On the other hand, Krawczyk's method is used to find regions in which solutions exist. As an illustrative example, all solutions of the nonlinear system of equations describing equilibrium conditions of the "high polymer liquid system", which is a well-known ill-conditioned system of equations, are identified by the method.
AB - A linear programming-based method is presented for finding all solutions of nonlinear systems of equations with guaranteed accuracy. In this method, a new effective linear programming-based method is used to delete regions in which solutions do not exist. On the other hand, Krawczyk's method is used to find regions in which solutions exist. As an illustrative example, all solutions of the nonlinear system of equations describing equilibrium conditions of the "high polymer liquid system", which is a well-known ill-conditioned system of equations, are identified by the method.
KW - All Solutions
KW - Guaranteed Accuracy
KW - Krawczyk's Method
KW - Linear Programming
KW - Nonlinear Equations
UR - http://www.scopus.com/inward/record.url?scp=0000146490&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0000146490&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0000146490
VL - 4
SP - 171
EP - 177
JO - Journal of Universal Computer Science
JF - Journal of Universal Computer Science
SN - 0948-695X
IS - 2
ER -