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• W2129784484 abstract "Structured linear algebra techniques are a versatile set of tools;they enable one to deal at once with various types of matrices, withfeatures such as Toeplitz-, Hankel-, Vandermonde- or Cauchy-likeness.Following Kailath, Kung and Morf (1979), the usual way of measuring towhat extent a matrix possesses one such structure is through itsdisplacement rank, that is, the rank of its image through a suitabledisplacement operator. Then, for the families of matrices given above,the results of Bitmead-Anderson, Morf, Kaltofen, Gohberg-Olshevsky,Pan (among others) provide algorithm of complexity $O(alpha^2 n)$, upto logarithmic factors, where $n$ is the matrix size and $alpha$ itsdisplacement rank.We show that for Toeplitz- Vandermonde-like matrices, this cost can bereduced to $O(alpha^(omega-1) n)$, where $omega$ is an exponent forlinear algebra. We present consequences for Hermite-Pad'e approximationand bivariate interpolation." @default.
• W2129784484 created "2016-06-24" @default.
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• W2129784484 date "2006-01-01" @default.
• W2129784484 modified "2023-09-26" @default.
• W2129784484 title "Using fast matrix multiplication to solve structured linear systems" @default.
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• W2129784484 hasPublicationYear "2006" @default.
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