Research on multi-core oriented parallel algorithms and implementation techniques for seminumerical processing

我们研究了将gpu和通用cpu的多核并行性应用于计算机代数或半数值算法的适当方法。具体而言，我们研究了大整数的RNS表示、多项式和线性代数的基本算法、隐函数绘制的精确方法、多项式插值，并在实证研究的基础上开发了面向多核的并行计算方法。作为相关主题，我们研究了交互式处理数学表达式的Web技术，并开发了一个gpu加速的魔方优化求解器。

We investigated appropriate methods to apply multi-core parallelism with GPUs and general-purpose CPUs to computer algebraic or seminumerical algorithms. More concretely, we treated RNS representation of big-integers, basic arithmetics of polynomials and in linear algebra, exact method for plotting implicit functions, polynomial interpolation, and developed multi-core oriented parallel computing methods for these topics based on empirical studies. As related topics, we investigated Web technology for treating mathematical expressions interactively, and developed a GPU-accelerated optimal solver for Rubik cubes.