The joint bidiagonalization (JBD) process iteratively reduces a matrix pair $\{A,B\}$ to two bidiagonal forms simultaneously, which can be used for computing a partial generalized singular value decomposition (GSVD) of $\{A,B\}$. The process has a nested inner-outer iteration structure, where the inner iteration usually can not be computed exactly. In this paper, we study the inaccurately computed inner iterations of JBD by first investigating influence of computational error of the inner iteration on the outer iteration, and then proposing a reorthogonalized JBD (rJBD) process to keep orthogonality of a part of Lanczos vectors. An error analysis of the rJBD is carried out to build up connections with Lanczos bidiabonalizations. The results are then used to investigate convergence and accuracy of the rJBD based GSVD computation. It is shown that the accuracy of computed GSVD components depend on the computing accuracy of inner iterations and condition number of $(A^T,B^T)^T$ while the convergence rate is not affected very much. For practical JBD based GSVD computations, our results can provide a guideline for choosing a proper computing accuracy of inner iterations in order to obtain approximate GSVD components with a desired accuracy. Numerical experiments are made to confirm our theoretical results.

翻译：联合调试( JBD) 进程迭接地将矩阵配对 $<unk> A, B<unk> $ 降为两个调试表格式, 可用于同时计算部分通用单值分解( GSVD) $<unk> A, B<unk> $美元。 这一过程有一个嵌入内部外转结构, 内部迭代通常无法精确计算。 在此文件中, 我们首先调查计算外转的内转误算的影响, 从而研究 JBD 的不准确内部迭代。 然后提议一个重新调整的 JBD (rJBD) 进程, 以保持兰乔斯矢量的一部分的局部通用单值分解( GSVD ) 进程。 对 rJBD 的错误分析, 以建立与兰乔斯代斯 标注的连接。 然后, 计算基于 GSVD 的 RJBD 组件的精度, 取决于对内转精确度的计算准确性, 以 USB 的精确度计算结果为基数 。 在基于 $B 的正确计算中, 的精度的精度计算中,, 能够获取我们精确的精度计算结果。</s>