Superfast Divide-and-Conquer Method and Perturbation Analysis for Structured Eigenvalue Solutions
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Publication:2805015
DOI10.1137/15M1018812zbMath1338.65104OpenAlexW2347093389MaRDI QIDQ2805015
James Vogel, Jian-Lin Xia, Stephen Cauley, Venkataramanan Balakrishnan
Publication date: 9 May 2016
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/15m1018812
compressionlinear complexityeigenvalue decompositionrank structurestructured perturbation analysissuperfast divide-and-conquer
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18)
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Cites Work
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- Transformations of matrix structures work again
- A fast algorithm for the inversion of general Toeplitz matrices
- A Divide and Conquer method for the symmetric tridiagonal eigenproblem
- Displacement ranks of matrices and linear equations
- Perturbations in eigenvalues
- Rank-one modification of the symmetric eigenproblem
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Construction and arithmetics of \(\mathcal H\)-matrices
- Introduction to hierarchical matrices with applications.
- A divide-and-conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semiseparable matrices
- A note on eigenvalues of perturbed Hermitian matrices
- Perturbation in eigenvalues of a symmetric tridiagonal matrix
- Eigenvalues of perturbed Hermitian matrices
- The QR iteration method for Hermitian quasiseparable matrices of an arbitrary order
- Superfast and Stable Structured Solvers for Toeplitz Least Squares via Randomized Sampling
- Computing All or Some Eigenvalues of Symmetric $\mathcal{H}_{\ell}$-Matrices
- On the Complexity of Some Hierarchical Structured Matrix Algorithms
- A Fast Randomized Eigensolver with Structured LDL Factorization Update
- Fast Sparse Selected Inversion
- A convergence analysis for a sweeping preconditioner for block tridiagonal systems of linear equations
- Fast algorithms for hierarchically semiseparable matrices
- On Computations with Dense Structured Matrices
- A Superfast Algorithm for Toeplitz Systems of Linear Equations
- A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
- A Fast Adaptive Multipole Algorithm for Particle Simulations
- Numerical Solution of the Eigenvalue Problem for Hermitian Toeplitz Matrices
- On the Orthogonality of Eigenvectors Computed by Divide-and-Conquer Techniques
- A Divide-and-Conquer Algorithm for the Bidiagonal SVD
- Stable and Efficient Algorithms for Structured Systems of Linear Equations
- Fast Gaussian Elimination with Partial Pivoting for Matrices with Displacement Structure
- A Superfast Structured Solver for Toeplitz Linear Systems via Randomized Sampling
- Relative Perturbation Bounds for Eigenvalues of Symmetric Positive Definite Diagonally Dominant Matrices
- Refined Perturbation Bounds for Eigenvalues of Hermitian and Non-Hermitian Matrices
- A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
- Efficient Structured Multifrontal Factorization for General Large Sparse Matrices
- A Fast Solver for HSS Representations via Sparse Matrices
- Some Fast Algorithms for Sequentially Semiseparable Representations
- Some Modified Matrix Eigenvalue Problems
- A fast algorithm for particle simulations
