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An efficient algorithm for global interval solution of nonlinear algebraic equations and its GPGPU implementation
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.Comment: 21pages, 1 figur