Cholesky分解递归算法与改进

递归算法是计算稠密线性代数的一种新的有效方法。递归产生自动、变化的矩阵分块，能充分发挥当今分级存储高性能计算机的效率。对Cholesky分解递归算法进行了研究，给出了算法的详细推导过程，用具有递归功能的Fortran90实现了算法，并通过矩阵元素顺序重排的方法，进一步提高了递归算法的运算速度。研究产生的算法比目前常用的分块算法快15％－25％。

RECURSIVE ALGORITHM AND IMPROVEMENT FOR CHOLESKY FACTORIZATION

Recursion is a new effective method for computing dense linear algebra. It allows for efficient utilization of memory hierarchies of today's high performance computers. The recursive algorithm for Cholesky factorization is studied in this paper. A detailed derivation of the recursive Cholesky algorithm is given. The algorithm is then implemented in Fortran 90 that supports recursion as a language feature. The efficiency of the recursive algorithm is further improved by using a method of matrix element reordering. The resulting algorithms are 15%~25% faster than the currently used block algorithm.