Details:
| Title | Algorithms for near solutions to polynomial equations | | Author(s) | Shih Ping Tung | | Type | Article in Journal | | Abstract | Let F ( x , y ) be a polynomial over a field K and m a nonnegative integer. We call a polynomial g over K an m -near solution of F ( x , y ) if there exists a c ∈ K such that F ( x , g ) = c x^m , and the number c is called an m -value of F ( x , y ) corresponding to g . In particular, c can be 0. Hence, by viewing F ( x , y ) = 0 as a polynomial equation over K [ x ] with variable y , every solution of the equation F ( x , y ) = 0 in K [ x ] is also an m -near solution. We provide an algorithm that gives all m -near solutions of a given polynomial F ( x , y ) over K , and this algorithm is polynomial time reducible to solving one variable equations over K . We introduce approximate solutions to analyze the algorithm. We also give some interesting properties of approximate solutions. | | Keywords | Algorithms, Near solution, Polynomial equations | | ISSN | 0747-7171 |
| URL |
http://www.sciencedirect.com/science/article/pii/S0747717109000765 |
| Language | English | | Journal | Journal of Symbolic Computation | | Volume | 44 | | Number | 10 | | Pages | 1410 - 1424 | | Year | 2009 | | Edition | 0 | | Translation |
No | | Refereed |
No |
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