- Estimating a matrix's singular values with interpolative decompositions
2025/11/21 by Anil Damle, Silke Glas, Alex Townsend +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Column (typography) #Exponential function #Gaussian #Matrix (chemical analysis) #QR decomposition #Selection (genetic algorithm) #Singular value #Singular value decomposition #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques
- Endpoint weak Schatten class estimates and trace formula for commutators of Riesz transforms with multipliers on Heisenberg groups
2023/10/04 by Zhijie Fan, Ji Li, Edward McDonald +2 · 2 citations
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Fourier transform #Heisenberg group #Integral equation #Law #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematics #Norm (philosophy) #Operator (biology) #Operator norm #Operator theory #Pure mathematics #Riesz transform #Singular integral #Singular value #Sobolev space #TRACE (psycholinguistics)
- Randomized Projection for Rank-Revealing Matrix Factorizations and Low-Rank Approximations
2020/01/01 by Jed A. Duersch, Ming Gu · 6 citations
Computer Science · Engineering · Mathematics · #Algorithm #Combinatorics #Computer science #Eigenvalues and eigenvectors #Low-rank approximation #Mathematics #Matrix (chemical analysis) #Matrix decomposition #Projection (relational algebra) #Pure mathematics #QR decomposition #Rank (graph theory) #Singular value #Singular value decomposition #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques #Tensor decomposition and applications
- An eigenvalue problem for even order tensors with its applications
2015/08/06 by Lu‐Bin Cui, Lu-Bin Cui, Chuan Chen +2 · 2 citations
Engineering · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Algorithm #Cartesian tensor #Circulant matrix #Combinatorics #Divide-and-conquer eigenvalue algorithm #Eigenvalues and eigenvectors #Elasticity and Material Modeling #Exact solutions in general relativity #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Order (exchange) #Physics #Pure mathematics #Singular value #Singular value decomposition #Tensor (intrinsic definition) #Tensor contraction #Tensor decomposition and applications #Tensor density #Tensor field #Tensor product #Toeplitz matrix #Transpose
- The limit of the smallest singular value of random matrices with i.i.d.\n entries
2014/10/23 by Konstantin Tikhomirov, Tikhomirov, Konstantin · 2 citations
Decision Sciences · Mathematics · #Combinatorics #Distribution (mathematics) #Eigenvalues and eigenvectors #FOS: Mathematics #Integer (computer science) #Limit (mathematics) #Mathematical analysis #Mathematics #Physics #Probability (math.PR) #Probability and Risk Models #Quantum mechanics #Random Matrices and Applications #Random matrix #Random variable #Sequence (biology) #Singular value #Spectral Theory in Mathematical Physics #Statistics #Unit (ring theory) #Zero (linguistics) #math.PR
- Most Tensor Problems Are NP-Hard
2013/11/01 by Christopher J. Hillar, Lek-Heng Lim, Lek‐Heng Lim · 180 citations
Computer Science · Mathematics · #Algebra over a field #Bilinear form #Bilinear interpolation #Cartesian tensor #Combinatorics #Eigenvalues and eigenvectors #Exact solutions in general relativity #Jordan algebra #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Matrix norm #Multilinear algebra #Multilinear map #Norm (philosophy) #Numerical Methods and Algorithms #Physics #Pure mathematics #Quantum mechanics #Rank (graph theory) #Singular value #Symmetric tensor #Tensor (intrinsic definition) #Tensor algebra #Tensor decomposition and applications #Tensor density #Tensor field
- Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions
2011/01/01 by N. Halko, Nathan Halko, P. G. Martinsson +3 · 609 citations
Computer Science · Engineering · Mathematics · #Algorithm #Computer science #Eigenvalues and eigenvectors #Hankel matrix #Low-rank approximation #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix completion #Matrix decomposition #QR decomposition #Randomized algorithm #Randomness #Singular value #Singular value decomposition #Sparse and Compressive Sensing Techniques #Sparse matrix #Stochastic Gradient Optimization Techniques #Tensor decomposition and applications
- A New Scaling for Newton's Iteration for the Polar Decomposition and its Backward Stability
2008/01/01 by Ralph Byers, Hongguo Xu · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Applied mathematics #Condition number #Convergence (economics) #Eigenvalues and eigenvectors #Geometry #Inverse #Iterative Methods for Nonlinear Equations #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix norm #Newton's method #Norm (philosophy) #Polar #Polar decomposition #Rate of convergence #Scalar (mathematics) #Scaling #Singular value #Singular value decomposition
- Numerical modelling of the spatial acoustic response of the human pinna
2005/11/30 by Yuvi Kahana, Philip A. Nelson, P.A. Nelson · 4 citations
Engineering · Mathematics · Neuroscience · #Acoustic Wave Phenomena Research #Acoustics #Algorithm #Boundary element method #Computer science #Computer vision #Cylinder #Field (mathematics) #Finite element method #Geometry #Hearing Loss and Rehabilitation #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Neuroscience and Music Perception #Physics #Pinna #Singular value #Singular value decomposition #Transfer matrix
- Fast monte-carlo algorithms for finding low-rank approximations
2004/11/01 by Alan Frieze, Ravi Kannan, Santosh Vempala · 46 citations
Computer Science · Engineering · Mathematics · #Algorithm #Combinatorics #Discrete mathematics #Hankel matrix #Low-rank approximation #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix norm #Matrix polynomial #Monte Carlo method #Polynomial #Polynomial matrix #Randomized algorithm #Rank (graph theory) #Singular value #Singular value decomposition #Sparse and Compressive Sensing Techniques #Statistics #Stochastic Gradient Optimization Techniques #Tensor decomposition and applications #Time complexity
- Products, Coproducts, and Singular Value Decomposition
2004/02/28 by Bertfried Fauser · 1 voice
Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic and Geometric Analysis #Algebraic structures and combinatorial models #Coproduct #Eigenvalues and eigenvectors #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Morphism #Singular value #Singular value decomposition #Tensor algebra #Tensor product #math-ph #math.MP #msc:15A18 #msc:15A66 #msc:16W30
- Scaled total least squares fundamentals
2002/03/01 by Christopher C. Paige, Zdenek Strakoš, Zdeněk Strakoš · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Combinatorics #Eigenvalues and eigenvectors #Estimator #Hermitian matrix #Least-squares function approximation #Limit (mathematics) #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Orthant #Overdetermined system #Physics #Pure mathematics #Quantum mechanics #Rank (graph theory) #Scientific Research and Discoveries #Singular value #Singular value decomposition #Statistical and numerical algorithms #Statistics #Total least squares #Uniqueness
- On the singular values of Gaussian random matrices
2001/03/01 by Jianhong Shen · 2 citations
Mathematics · #Advanced Combinatorial Mathematics #Algorithm #Cholesky decomposition #Eigenvalues and eigenvectors #Gaussian #Mathematical analysis #Mathematics #Multivariate statistics #Orthogonal group #Pure mathematics #Quadrant (abdomen) #Quantum mechanics #Random Matrices and Applications #Random matrix #Singular value #Singular value decomposition #Statistics #Stochastic processes and statistical mechanics #Wishart distribution
- Locally Toeplitz sequences: spectral properties and applications
1998/07/01 by P. Tilli, Paolo Tilli · 20 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Bounded function #Combinatorics #Distribution (mathematics) #Eigenvalues and eigenvectors #Hermitian matrix #Holomorphic and Operator Theory #Levinson recursion #Mathematical analysis #Mathematics #Pure mathematics #Random Matrices and Applications #Sequence (biology) #Singular value #Toeplitz matrix
- Structured total least squares and L2 approximation problems
1993/07/01 by Bart De Moor · 5 citations
Computer Science · Engineering · Mathematics · #Algorithm #Applied mathematics #Control Systems and Identification #Convergence (economics) #Eigenvalues and eigenvectors #Estimation theory #Generalized least squares #Image and Signal Denoising Methods #Inverse #Kalman filter #Least-squares function approximation #Mathematics #Non-linear least squares #Realization (probability) #Singular value #Singular value decomposition #Statistical and numerical algorithms #Statistics #Total least squares
- Accurate Singular Values of Bidiagonal Matrices
1990/09/01 by James Demmel, W. Kahan · 3 citations
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Scientific Research and Discoveries #Statistical and numerical algorithms #Mathematics #Singular value #Singular value decomposition #Singular solution #Matrix (chemical analysis) #Applied mathematics #Algorithm #Mathematical analysis #Eigenvalues and eigenvectors
- Nearly weakly orthonormal sequences, singular value estimates, and Calderon-Zygmund operators
1989/10/01 by Richard Rochberg, Stephen Semmes · 8 citations
Mathematics · #Advanced Harmonic Analysis Research #Algorithm #Combinatorics #Eigenvalues and eigenvectors #Holomorphic and Operator Theory #Mathematics #Multiplication (music) #Operator (biology) #Operator theory #Orthonormal basis #Pure mathematics #Rank (graph theory) #Singular value #Singular value decomposition #Spectral Theory in Mathematical Physics #Statistics #TRACE (psycholinguistics) #Value (mathematics)
- The truncatedSVD as a method for regularization
1987/12/01 by Per Christian Hansen · 2 citations
Computer Science · Mathematics · #Algorithm #Applied mathematics #Artificial intelligence #Combinatorics #Computer science #Eigenvalues and eigenvectors #Linear least squares #Mathematical optimization #Mathematics #Matrix Theory and Algorithms #Numerical methods in inverse problems #Physics #Rank (graph theory) #Regularization (linguistics) #Singular value #Singular value decomposition #Statistical and numerical algorithms
- Truncated balanced realization of a stable non-minimal state-space system
1987/10/01 by Michael Tombs, M. S. TOMBS, Ian Postlethwaite +1 · 5 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Combinatorics #Computer science #Control (management) #Control theory (sociology) #Eigenvalues and eigenvectors #Geometry #Hankel matrix #Linear system #Lyapunov function #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Minimal realization #Model Reduction and Neural Networks #Multiplication (music) #Numerical methods for differential equations #Probabilistic and Robust Engineering Design #Realization (probability) #Reduction (mathematics) #Singular value #Singular value decomposition #State (computer science) #State space #Unobservable
- Some distance properties of latent root and vector methods used in multivariate analysis
1966/01/01 by J. C. GOWER, J. C. Gower · 128 citations
Agricultural and Biological Sciences · Chemistry · Mathematics · #Advanced Statistical Methods and Models #Combinatorics #Eigenvalues and eigenvectors #Euclidean distance #Euclidean distance matrix #Euclidean space #Geometry #Interpretation (philosophy) #Mathematics #Matrix (chemical analysis) #Multivariate statistics #Point (geometry) #Principal component analysis #Representation (politics) #Sample (material) #Sensory Analysis and Statistical Methods #Set (abstract data type) #Singular value #Spectroscopy and Chemometric Analyses #Statistics
- Calculating the Singular Values and Pseudo-Inverse of a Matrix
1965/01/01 by Gene H. Golub, W. Kahan · 11 citations
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Electromagnetic Scattering and Analysis #Scientific Research and Discoveries #Diagonal #Unitary matrix #Spurious relationship #Matrix (chemical analysis) #Mathematics #Inverse #Sigma #Unitary state #Diagonal matrix #Singular value #Cover (algebra) #Scheme (mathematics) #Applied mathematics #Algorithm #Mathematical analysis #Physics #Eigenvalues and eigenvectors #Geometry #Statistics
- Inversion of Matrices by Biorthogonalization and Related Results
1958/03/01 by Magnus R. Hestenes · 3 citations
Computer Science · Mathematics · #Matrix Theory and Algorithms #Advanced Optimization Algorithms Research #Numerical Methods and Algorithms #Tridiagonal matrix #Singular value decomposition #Algorithm #Jacobi method #Computation #Singular value #Matrix (chemical analysis) #Computer science #Mathematics #Algebra over a field #Applied mathematics #Pure mathematics #Physics