论文标题
计算符号$ ll^t $分解
On computing the symplectic $LL^T$ factorization
论文作者
论文摘要
我们分析了两种用于计算给定对称正定确定符号矩阵$ a $的符合$ ll^t $分解的算法。第一个算法$ W_1 $是[Dopico等，2009]的$ HH^T $分解的实现，请参见定理5.2。第二个算法$ w_2 $使用对称正定矩阵的cholesky和Cholesky和Chorversky的分解。我们对这些算法进行了比较，并通过MATLAB中的数值实验说明了它们的性质。浮点算术中计算出的矩阵的简单性特性给出了特别的重点。
We analyze two algorithms for computing the symplectic $LL^T$ factorization $A=LL^T$ of a given symmetric positive definite symplectic matrix $A$. The first algorithm $W_1$ is an implementation of the $HH^T$ factorization from [Dopico et al., 2009], see Theorem 5.2. The second one, algorithm $W_2$ uses both Cholesky and Reverse Cholesky decompositions of symmetric positive definite matrices. We presents a comparison of these algorithms and illustrate their properties by numerical experiments in MATLAB. A particular emphasis is given on simplecticity properties of the computed matrices in floating-point arithmetic.
