Structure-preserving joint Lanczos bidiagonalization with thick-restart for the partial quaternion GSVD

A new Krylov subspace method is designed in the computation of partial quaternion generalized singular value decomposition (QGSVD) of a large-scale quaternion matrix pair \(\{\textbf{A}, \textbf{B}\}\). Explicitly, we present the structure-preserving joint Lanczos bidiagonalization method to reduce \(\textbf{A}\) and \(\textbf{B}\) to lower and upper real bidiagonal matrices, respectively. We carry out the thick-restarted technique with the combination of a robust selective reorthogonalization strategy in the structure-preserving joint Lanczos bidiagonalization process. In the iteration process we avoid performing the explicit QR decomposition of the quaternion matrix pair. Numerical experiments illustrate the effectiveness of the proposed method.