论文标题
用于计算大矩阵对的部分广义奇异值分解（GSVD）的跨产品免费jacobi-davidson类型
A cross-product free Jacobi-Davidson type method for computing a partial generalized singular value decomposition (GSVD) of a large matrix pair
论文作者
论文摘要
提出了一种跨产品（CPF）Jacobi-Davidson（JD）类型方法来计算大型常规矩阵对$（A，B）$的部分广义奇异值分解（GSVD）。它隐含地解决了$（a^ta，b^tb）$的数学上等效特征值问题，但并未明确形成交叉产品矩阵，因此避免了计算出的广义奇异值的准确性损失和广义的单数矢量。该方法是一种内部迭代方法，其中右搜索子空间的扩展形成内部迭代，该迭代近似求解所涉及的校正方程，外迭代提取了相对于子空间的近似GSVD组件。基于某些实用停止标准是为内部迭代设计的，为内部和外迭代建立了一些收敛结果。开发了一种带有通气的厚的CPF-JDGSVD算法，以计算几个GSVD组件。数值实验说明了算法的效率。
A Cross-Product Free (CPF) Jacobi-Davidson (JD) type method is proposed to compute a partial generalized singular value decomposition (GSVD) of a large regular matrix pair $(A,B)$. It implicitly solves the mathematically equivalent generalized eigenvalue problem of $(A^TA,B^TB)$ but does not explicitly form the cross-product matrices and thus avoids the possible accuracy loss of the computed generalized singular values and generalized singular vectors. The method is an inner-outer iteration method, where the expansion of the right searching subspace forms the inner iterations that approximately solve the correction equations involved and the outer iterations extract approximate GSVD components with respect to the subspaces. Some convergence results are established for the inner and outer iterations, based on some of which practical stopping criteria are designed for the inner iterations. A thick-restart CPF-JDGSVD algorithm with deflation is developed to compute several GSVD components. Numerical experiments illustrate the efficiency of the algorithm.
