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Solving nonlinear algebraic equations is a classic mathematics problem, andcommon in scientific researches and engineering applications. There are manynumeric, 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 isdecreasing drastically. In this paper, according to the property of physicalworld, we pay attention to nonlinear algebraic equations whose variables are infixed constraints, and get meaningful real solutions. Combining withparallelism of GPGPU, we present an efficient algorithm, by searching thesolution space globally and solving the nonlinear algebraic equations with realinterval solutions. Furthermore, we realize the Hansen-Sengupta method onGPGPU. The experiments show that our method can solve many nonlinear algebraicequations, and the results are accurate and more efficient compared totraditional serial methods.

An efficient algorithm for global interval solution of nonlinear algebraic equations and its GPGPU implementation