LU分解递归算法的实现

§1.引言 以LU分解, Cholesky分解等为代表的线性代数问题的数值计算在现代科学研究和工程技术中得到广泛应用.随着计算机技术的发展,实现这些线性代数数值计算的计算机算法和软件也在不断发展.目前,具有多级存储结构的高性能RISC计算机已占据了数值计算领域的主导地位. RSIC处理器的运算速度非常快,它们与存储器之间的速度差距很大.计算机的性能能不能充分发挥,多级存储结构与高缓能否得到有效利用成为关键.为此,现行的

IMPLEMENTATION OF RECURSIVE ALGORITHM FOR LU FACTORIZATION

Recursion leads to automatic matrix blocking in the computation of dense linear algebra. It makes a good use of memory hierarchies of today's high-performance computers and hence improves the efficiency of the algorithm. The recursive algorithm for LU factorization of matrix that is used to solve linear systems of equations is studied in this paper. A detailed derivation of the recursive algorithm is presented. FORTRAN90 language, which supports recursion as a language feature, is used to implement the algorithm. Experimental results show that the recursive algorithm is near 20% faster than the currently used block algorithm.