On a new class of structured matrices

By Yuli Eidelman, Israel Gohberg. 1999

Subfields: Numerical Methods & Scientific Computing

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Citations in the corpus

A modification of the Dewilde-van der Veen method for inversion of finite structured matrices (2002, background): “We started the detailed study of this class in our paper [5].”
Monarch: Expressive Structured Matrices for Efficient and Accurate Training (2022, background): “, Toeplitz-like [95], orthogonal polynomial transforms [25], low-displacement rank [53], quasi-separable [27]), though learnable, often lack efficient implementation on GPUs [98] for E2E training as well.”
Low-rank tensor structure of linear diffusion operators in the TT and QTT formats☆ (2013, background): “This condition is well-known in the theory of quasi-separable matrices (see, e. g., [9]) and means that the matrix A is quasi-separable of order r .”
Fast algorithms for hierarchically semiseparable matrices (2010, unknown): “…systems [ 1–4 ] , least squares problems [ 5 ] , eigenvalue problems [ 6–11 ] , PDEs [ 12–15 ] , integral equations [ 16–18 ] , etc. Examples of rank-structured matrices include H -matrices [ 19–21 ] , H 2 -matrices [ 22–24 ] , quasiseparable matrices [ 25 ] , and semiseparable matrices [ 26–28 ] .”
A Two-pronged Progress in Structured Dense Matrix Vector Multiplication (2018, background): “Just as how the four main displacement structures are closely tied to polynomial operations [44], the work of Bella, Eidelman, Gohberg, and Olshevsky show deep connections between computations with rank-structured matrices and with polynomials [7].”
ON THE SHIFTED QR ITERATION APPLIED TO COMPANION MATRICES (2004, background): “Semiseparable matrices are closely related to the inverses of banded matrices and have further nice properties which relate them to their inverses and to their LU and QR factorizations (see [5], [6], [7], [9], [11], [12], [13], [14], [16], [17] and the references therein).”
A bibliography on semiseparable matrices* (2005, background): “For example one can easily verify that every diagonal matrix is a semiseparable matrix, but not a generator representable semiseparable matrix (except in special cases).”
Combining Recurrent, Convolutional, and Continuous-time Models with Linear State-Space Layers (2021, unknown): “Deﬁnition 4 (from [19]) .”