Paper Info
Title
An efficient algorithm for global interval solution of nonlinear algebraic equations and its GPGPU implementation.
Abstract
Solving nonlinear algebraic equations is a classic mathematics problem, and common in scientific researches and engineering applications. There are many numeric, symbolic and numeric-symbolic methods of solving (real) solutions. Unlucky, these methods are constrained by some factors, e.g., high complexity, slow serial calculation, and the notorious intermediate expression expansion. Especially when the count of variables is larger than six, the efficiency is decreasing drastically. In this paper, according to the property of physical world, we pay attention to nonlinear algebraic equations whose variables are in fixed constraints, and get meaningful real solutions. Combining with parallelism of GPGPU, we present an efficient algorithm, by searching the solution space globally and solving the nonlinear algebraic equations with real interval solutions. Furthermore, we realize the Hansen-Sengupta method on GPGPU. The experiments show that our method can solve many nonlinear algebraic equations, and the results are accurate and more efficient compared to traditional serial methods.
Year
Venue
Field
2018
arXiv: Numerical Analysis
Nonlinear system,Algorithm,Algebraic equation,General-purpose computing on graphics processing units,Mathematics
DocType
Volume
Citations 
Journal
abs/1802.00330
0
PageRank 
References 
Authors
0.34
5
2
Name
Order
Citations
PageRank
Dang Lin100.68
Liangyu Chen205.75