论文标题
两种用于计算大型基质对的部分广义奇异值分解的谐波雅各比 - 戴维森方法
Two harmonic Jacobi--Davidson methods for computing a partial generalized singular value decomposition of a large matrix pair
论文作者
论文摘要
提出了两种基于谐波的雅各比 - 戴维森（JD）型算法来计算大型常规矩阵对的部分广义奇异值分解（GSVD）。它们被称为跨产品（CPF）和无逆（IF）谐波JDGSVD算法，分别缩写为CPF-HJDGSVD和IF-HJDGSVD。与基于标准提取的JDGSVD算法相比，基于谐波提取的算法更定期收敛，并且更适合计算与内部广义奇异值相对应的GSVD组件。开发了具有某些放气和炼狱技术的较厚的CPF-HJDGSVD和IF-HJDGSVD算法，以计算多个GSVD组件。数值实验证实了CPF-HJDGSVD和IF-HJDGSVD对基于标准提取的JDGSVD算法的优越性。
Two harmonic extraction based Jacobi--Davidson (JD) type algorithms are proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair. They are called cross product-free (CPF) and inverse-free (IF) harmonic JDGSVD algorithms, abbreviated as CPF-HJDGSVD and IF-HJDGSVD, respectively. Compared with the standard extraction based JDGSVD algorithm, the harmonic extraction based algorithms converge more regularly and suit better for computing GSVD components corresponding to interior generalized singular values. Thick-restart CPF-HJDGSVD and IF-HJDGSVD algorithms with some deflation and purgation techniques are developed to compute more than one GSVD components. Numerical experiments confirm the superiority of CPF-HJDGSVD and IF-HJDGSVD to the standard extraction based JDGSVD algorithm.
