This paper considers a novel structure-preserving method for solving non-Hermitian quaternion linear systems arising from color image deblurred problems. From the quaternion Lanczos biorthogonalization procedure that preserves the quaternion tridiagonal form at each iteration, we derive the quaternion biconjugate gradient method for solving the linear systems and then establish the convergence analysis of the proposed algorithm. Finally, we provide some numerical examples to illustrate the feasibility and validity of our method in comparison with the QGMRES, especially in terms of computing time.

This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor equations. A theoretical analysis shows that the proposed method converges to an exact solution for any initial tensor at most finite steps in the absence round-off errors. Compared with a modified conjugate gradient method, the obtained numerical results illustrate that our methods perform much better in terms of the number of iteration steps and computing time.

Summary: ‘ Candidatus Liberibacter asiaticus’ (CLas) is a phloem‐limited non‐culturable α‐proteobacterium associated with citrus Huanglongbing, a highly destructive disease threatening global citrus industry. Research on CLas is challenging due to the current inability to culture CLas in vitro and the low CLas titre in citrus plant. Here, we develop a CLas enrichment system using the holoparasitic dodder plant ( Cuscuta campestris ) as an amenable host to acquire and enrich CLas from CLas‐infected citrus shoots maintained hydroponically. Forty‐eight out of fifty‐five (87%) dodder plants successfully parasitized CLas‐infected citrus shoots with detectable CLas by PCR. Among 48 dodders cultures, 30 showed two‐ to 419‐fold CLas titre increase as compared to the corresponding citrus hosts. The CLas population rapidly increased and reached the highest level in dodder tendrils at 15 days after parasitizing citrus shoot. Genome sequencing and assembly derived from CLas‐enriched dodder DNA samples generated a higher resolution than those obtained for CLas from citrus hosts. No genomic variation was detected in CLas after transmission from citrus to dodder during short‐term parasitism. Dual RNA‐Seq experiments showed similar CLas gene expression profiles in dodder and citrus samples, yet dodder samples generated a higher resolution of CLas transcriptome data. The ability of dodder to support CLas multiplication to high levels, as well as its advantage in CLas genomic and transcriptomic analyses, make it an optimal model for further studies on CLas–host interaction.

This paper is concerned with the iterative solutions to a class of generalized Sylvester quaternion tensor equations. From the Kronecker product and the properties of quaternion tensors, we propose the biconjugate A-orthogonal residual stabilized and the generalized product-type biconjugate A-orthogonal residual methods in their tensor forms for solving the original tensor equation. As an application, the proposed methods are tested with some colour video restoration problems. Numerical results show the effectiveness of our methods compared with some existing methods.