Abstract
The fact that nonsingular coefficient matrices can be covered by blocks close to low-rank matrices is well known probably for years. It was used in some cost-effective matrix-vector multiplication algorithms. However, it has been never paid a proper attention in the matrix theory. To fill in this gap we propose a notion of mosaic ranks of a matrix which reduces a description of block matrices with low-rank blocks to a single number. A general algebraic framework is presented that allows one to obtain some theoretical estimates on the mosaic ranks. An algorithm for computing upper estimates of the mosaic ranks is given with some illustrations of its efficiency on model problems.
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© 1997 Springer-Verlag Berlin Heidelberg
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Tyrtyshnikov, E. (1997). Mosaic ranks and skeletons. In: Vulkov, L., Waśniewski, J., Yalamov, P. (eds) Numerical Analysis and Its Applications. WNAA 1996. Lecture Notes in Computer Science, vol 1196. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62598-4_132
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DOI: https://doi.org/10.1007/3-540-62598-4_132
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