论文标题
与部分重新定义的联合竞争者合作过程
The joint bidiagonalization process with partial reorthogonalization
论文作者
论文摘要
联合竞技表结构（JBD）过程是用于计算矩阵对的广义奇异值分解（GSVD）的有用算法。但是，它始终遭受舍入错误，这会导致兰开斯向量失去相互正交性。为了维持一定程度的矫正性，我们提出了一种半指导策略。我们的四舍五入错误分析表明，具有半双轴化策略的JBD过程可以确保计算数量的收敛性不受舍入误差的影响，并且最终的准确性足够高。基于半双轴化策略，我们通过部分重新构化（JBDPRO）开发了联合竞争性过程。在JBDPRO算法中，仅在必要时才会进行重新定位，这与完整的重新配合策略相比节省了大量的重新批量工作。数值实验说明了我们的理论和算法。
The joint bidiagonalization(JBD) process is a useful algorithm for the computation of the generalized singular value decomposition(GSVD) of a matrix pair. However, it always suffers from rounding errors, which causes the Lanczos vectors to loss their mutual orthogonality. In order to maintain some level of orthongonality, we present a semiorthogonalization strategy. Our rounding error analysis shows that the JBD process with the semiorthogonalization strategy can ensure that the convergence of the computed quantities is not affected by rounding errors and the final accuracy is high enough. Based on the semiorthogonalization strategy, we develop the joint bidiagonalization process with partial reorthogonalization(JBDPRO). In the JBDPRO algorithm, reorthogonalizations occur only when necessary, which saves a big amount of reorthogonalization work compared with the full reorthogonalization strategy. Numerical experiments illustrate our theory and algorithm.
