Toeplitz
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Block Jacobi/Gauss-Seidel preconditioning for GLT sequences, and GLH sequences
arXiv:2606.01888v1 Announce Type: new Abstract: The theory of generalized locally Toeplitz (GLT) sequences is an apparatus for computing the spectral and singular value distribution of sequences of matrices that possess a (possibly hidden) Toeplitz-like structure.
Structure-Informed Bounds on the Kronecker Rank of Block-Structured Matrices
arXiv:2605.30908v1 Announce Type: new Abstract: We derive theoretical bounds on the Kronecker rank of block-structured matrices that possess both inner and outer structure. Building on the matrix-to-tensor and tensor-to-matrix framework of Kilmer and Saibaba ($\textit{SIAM J. Matrix Anal.
Solving Coupled Tensor Equation $\mathcal{A} \ltimes \mathcal{X} =\mathcal{B}, \ \mathcal{X}\ltimes \mathcal{C}=\mathcal{D}$ using Semi-Tensor Products in the t-product
arXiv:2605.31122v1 Announce Type: new Abstract: This paper investigates the solution of coupled third-order tensor equation $\mathcal{A} \ltimes \mathcal{X} = \mathcal{B},\ \mathcal{X} \ltimes \mathcal{C} = \mathcal{D},$ of arbitrary dimensions by incorporating semi-tensor product (STP) within t-product framework, where the unknown $\mathcal{X}$ can take form of vector, matrix, or tensor. For the unknown $\mathcal{X}$, we establish a necessary and sufficient condition that provides an...