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• W2070581206 abstract "For a given symmetric positive definite matrix $Ainmathbf{R}^{Ntimes N}$, we develop a fast and backward stable algorithm to approximate A by a symmetric positive definite semiseparable matrix, accurate to a constant multiple of any prescribed tolerance. In addition, this algorithm preserves the product, $AZ$, for a given matrix $Zinmathbf{R}^{Ntimes d}$, where $dll N$. Our algorithm guarantees the positive-definiteness of the semiseparable matrix by embedding an approximation strategy inside a Cholesky factorization procedure to ensure that the Schur complements during the Cholesky factorization all remain positive definite after approximation. It uses a robust direction-preserving approximation scheme to ensure the preservation of $AZ$. We present numerical experiments and discuss the potential implications of our work." @default.
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• W2070581206 date "2010-01-01" @default.
• W2070581206 modified "2023-09-27" @default.
• W2070581206 title "Direction-Preserving and Schur-Monotonic Semiseparable Approximations of Symmetric Positive Definite Matrices" @default.
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• W2070581206 doi "https://doi.org/10.1137/090774331" @default.
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