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Matrices with Hierarchical Low-Rank Structures (Q2971626)

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Language	Label	Description	Also known as
English	Matrices with Hierarchical Low-Rank Structures	scientific article

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scholarly article

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Matrices with Hierarchical Low-Rank Structures (English)

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zbMATH Open document ID

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10.1007/978-3-319-49887-4_3

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Daniel Kressner

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Lecture Notes in Mathematics

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publication date

7 April 2017

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Mathematics Subject Classification ID

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zbMATH DE Number

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zbMATH Keywords

singular value decomposition

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matrix compression

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block partitioning

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low-rank structures

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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full work available at URL

https://doi.org/10.1007/978-3-319-49887-4_3

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A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite‐element matrices

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Matrices with Hierarchical Low-Rank Structures

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Factorized solution of Lyapunov equations based on hierarchical matrix arithmetic

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Approximation of boundary element matrices

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On the purely algebraic data-sparse approximation of the inverse and the triangular factors of sparse matrices

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Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients

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Adaptive low-rank approximation of collocation matrices

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Comparison of Some Reduced Representation Approximations

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The condition number of real Vandermonde, Krylov and positive definite Hankel matrices

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Computing All or Some Eigenvalues of Symmetric $\mathcal{H}_{\ell}$-Matrices

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The preconditioned inverse iteration for hierarchical matrices

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Computing the eigenvalues of symmetric \(\mathcal{H}^2\)-matrices by slicing the spectrum

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Decay bounds and \(O(n)\) algorithms for approximating functions of sparse matrices

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Hybrid cross approximation of integral operators

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Exponential inapproximability of selecting a maximum volume sub-matrix

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Some Fast Algorithms for Sequentially Semiseparable Representations

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Sublinear Randomized Algorithms for Skeleton Decompositions

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On selecting a maximum volume sub-matrix of a matrix and related problems

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An \(O(N)\) direct solver for integral equations on the plane

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Direct Methods for Sparse Linear Systems

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Decay Rates for Inverses of Band Matrices

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Computing the singular value decomposition with high relative accuracy

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New Fast and Accurate Jacobi SVD Algorithm. I

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\(\mathcal H\)-matrix approximation for the operator exponential with applications

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An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling

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A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains

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A Block Lanczos Method for Computing the Singular Values and Corresponding Singular Vectors of a Matrix

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A theory of pseudoskeleton approximations

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Solution of large scale algebraic matrix Riccati equations by use of hierarchical matrices

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A fast algorithm for particle simulations

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Fast direct solvers for integral equations in complex three-dimensional domains

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A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices

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Hierarchical Matrices: Algorithms and Analysis

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New estimates for the recursive low-rank truncation of block-structured matrices

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Hierarchical matrices based on a weak admissibility criterion

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Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions

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On the low-rank approximation by the pivoted Cholesky decomposition

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ARPACK Users' Guide

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The generalized empirical interpolation method: stability theory on Hilbert spaces with an application to the Stokes equation

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A fast direct solver for boundary integral equations in two dimensions

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An algebraic multifrontal preconditioner that exploits the low‐rank property

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Fast Hierarchical Solvers For Sparse Matrices Using Extended Sparsification and Low-Rank Approximation

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Approximation rates for the hierarchical tensor format in periodic Sobolev spaces

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Low-Rank Matrix Approximation Using the Lanczos Bidiagonalization Process with Applications

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Incomplete cross approximation in the mosaic-skeleton method

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A note on the representation and definition of semiseparable matrices

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Superfast Divide-and-Conquer Method and Perturbation Analysis for Structured Eigenvalue Solutions

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A Parallel Geometric Multifrontal Solver Using Hierarchically Semiseparable Structure

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Perturbation bounds in connection with singular value decomposition

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Fast algorithms for hierarchically semiseparable matrices

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Mathematics(1 entry)

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