- Fast Matrix Square Roots with Applications to Gaussian Processes and Bayesian Optimization
2020/06/19 by Geoff Pleiss, Pleiss, Geoff, Martin Jankowiak +7 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Bayesian probability #Combinatorics #Computation #Computer science #Covariance matrix #Eigenvalues and eigenvectors #FOS: Computer and information sciences #Gaussian #Gaussian Processes and Bayesian Inference #Gibbs sampling #Iterative method #Krylov subspace #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Mathematics #Matrix (chemical analysis) #Model Reduction and Neural Networks #Multiplication (music) #Physics #Quadratic equation #Quantum mechanics #Sampling (signal processing) #Scientific Research and Discoveries #Square matrix #Statistics #Symmetric matrix #cs.LG #stat.ML
- Simple, Double and Isoclinic Rotations with a Viable Algorithm
2020/02/19 by Melek Erdoğdu, Mustafa Özdemir · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Matrix Theory and Algorithms #Mathematics and Applications #Advanced Mathematical Theories and Applications #Skew-symmetric matrix #Rotation (mathematics) #Simple (philosophy) #Mathematics #Skew #Matrix (chemical analysis) #Rotation matrix #Eigenvalues and eigenvectors #Pure mathematics #Euclidean space #Euler's rotation theorem #Symmetric matrix #Combinatorics #Square matrix #Computer science #Geometry #Physics
- Characterizations of k-commutative equalities for some outer generalized inverses
2018/07/26 by D. E. Ferreyra, F. E. Levis, F. E. Levis +2 · 4 citations
Computer Science · Engineering · Mathematics · #Algebra over a field #Commutative property #Control Systems and Identification #Core (optical fiber) #Eigenvalues and eigenvectors #Generalized inverse #Geometry #Inverse #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Moore–Penrose pseudoinverse #Pure mathematics #Space (punctuation) #Square (algebra) #Square matrix #Stability and Control of Uncertain Systems #Symmetric matrix
- Improved Rectangular Matrix Multiplication using Powers of the Coppersmith-Winograd Tensor
2017/08/31 by François Le Gall, Florent Urrutia · 3 citations
Computer Science · Mathematics · #Arithmetic #Combinatorics #Complexity and Algorithms in Graphs #Discrete mathematics #Geometry #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Multiplication (music) #Parallel Computing and Optimization Techniques #Physics #Pure mathematics #Square (algebra) #Square matrix #Symmetric matrix #Tensor (intrinsic definition) #Tensor decomposition and applications #Tensor product #acm:65F60 #acm:68Q25 #cs.CC #cs.DS #msc:65F60 #msc:68Q25
- Accelerating a recurrent neural network to finite-time convergence using a new design formula and its application to time-varying matrix square root
2017/06/30 by Lin Xiao · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Algorithms and Applications #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Computer science #Convergence (economics) #Engineering #Geometry #Iterative Learning Control Systems #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Neural Networks and Applications #Physics #Root (linguistics) #Root mean square #Square (algebra) #Square matrix #Square root #Symmetric matrix #Zhàng
- On a new generalized inverse of matrices
2017/06/14 by Mahboobeh Mehdipour, Abbas Salemi · 7 citations
Chemistry · Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Algebra over a field #Algebra representation #Chemistry #Combinatorics #Division algebra #Eigenvalues and eigenvectors #Generalized inverse #Geometry #Inverse #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Moore–Penrose pseudoinverse #Multilinear algebra #Multilinear map #Physics #Pure mathematics #Square matrix #Symmetric matrix #graph theory and CDMA systems
- Computational Methods for Linear Matrix Equations
2016/01/01 by V. Simoncini, Valeria Simoncini · 50 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Applied mathematics #Eigenvalues and eigenvectors #Electromagnetic Scattering and Analysis #Linear equation #Materials science #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Numerical analysis #Numerical linear algebra #Numerical methods for differential equations #Physics #Pure mathematics #Square matrix #Symmetric matrix
- The bipolar decomposition
2013/09/18 by Rajendra Bhatia · 2 citations
Computer Science · Engineering · Mathematics · #Algebra over a field #Combinatorics #Decomposition #Eigenvalues and eigenvectors #Geometry #Invertible matrix #Mathematical proof #Mathematics #Mathematics and Applications #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix decomposition #Positive-definite matrix #Pure mathematics #Skew-symmetric matrix #Square matrix #Symmetric matrix #Unitary matrix #Unitary state #graph theory and CDMA systems
- Blocked Schur Algorithms for Computing the Matrix Square Root
2013/01/01 by Edvin Deadman, Nicholas J. Higham, Rui Ralha · 1 citation
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #Algorithm #Blocking (statistics) #Computation #Computer science #Geometry #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix multiplication #Parallel Computing and Optimization Techniques #Parallel computing #Pure mathematics #Sparse matrix #Square (algebra) #Square matrix #Square root #Square root of a 2 by 2 matrix #Symmetric matrix #Triangular matrix
- Sums of two triangularizable quadratic matrices over an arbitrary field
2011/09/30 by Clément de Seguins Pazzis · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Topics in Algebra #Combinatorics #Discrete mathematics #Eigenvalues and eigenvectors #Field (mathematics) #Finite field #Geometry #Idempotence #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Physics #Pure mathematics #Quadratic equation #Quadratic form (statistics) #Square (algebra) #Square matrix #Symmetric matrix #Zero (linguistics) #graph theory and CDMA systems #math.RA #msc:15A24 #msc:15B33
- The solution of linear systems by using the Sherman–Morrison formula
2006/09/13 by P. Maponi, Pierluigi Maponi · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Coefficient matrix #Combinatorics #Eigenvalues and eigenvectors #Electromagnetic Scattering and Analysis #Geometry #Inverse #Invertible matrix #Linear system #M-matrix #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Moore–Penrose pseudoinverse #Pure mathematics #Rank (graph theory) #Scientific Research and Discoveries #Square matrix #Symmetric matrix
- Generalized Inverses
2003/01/01 by Adi Ben-Israel, T. N. E. Greville · 4 citations
Chemistry · Computer Science · Mathematics · #Chemistry #Combinatorics #Eigenvalues and eigenvectors #Generalized inverse #Geometry #Identity matrix #Inverse #Invertible matrix #Involutory matrix #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Physics #Pure mathematics #Square matrix #Symmetric matrix
- On the Rigid Rotation Concept in n-Dimensional Spaces
2001/09/01 by Daniele Mortari · 2 citations
Computer Science · Engineering · Mathematics · #Euler angles #Geometry #Geophysics and Sensor Technology #Hermitian matrix #Inertial Sensor and Navigation #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Orthogonal basis #Orthogonal matrix #Physics #Pure mathematics #Rotation (mathematics) #Rotation matrix #Skew-symmetric matrix #Square matrix #Symmetric matrix
- Approximating the Logarithm of a Matrix to Specified Accuracy
2001/01/01 by Sheung Hun Cheng, Nicholas J. Higham, Charles Kenney +1 · 2 citations
Computer Science · Physics and Astronomy · Mathematics · #Matrix Theory and Algorithms #Numerical Methods and Algorithms #Electromagnetic Scattering and Analysis #Mathematics #Square root #Square matrix #Logarithm #Matrix (chemical analysis) #Computation #Matrix multiplication #Applied mathematics #Algorithm #Symmetric matrix #Mathematical analysis #Geometry
- Stable iterations for the matrix square root
1997/09/01 by Nicholas J. Higham · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Eigenvalues and eigenvectors #Electromagnetic Scattering and Analysis #Geometry #Invertible matrix #Iterative method #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Numerical methods for differential equations #Power iteration #Preconditioner #Pure mathematics #Quadratic growth #Sign (mathematics) #Square (algebra) #Square matrix #Square root #Symmetric matrix #Theory of computation
- Fast Polar Decomposition of an Arbitrary Matrix
1990/07/01 by Nicholas J. Higham, Robert Schreiber · 6 citations
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #Numerical Methods and Algorithms #Inertial Sensor and Navigation #Mathematics #Hermitian matrix #Matrix (chemical analysis) #Matrix multiplication #Positive-definite matrix #Block matrix #Algorithm #Cholesky decomposition #LU decomposition #Polar decomposition #Matrix decomposition #Matrix splitting #Sparse matrix #Newton's method #Iterative method #Symmetric matrix #Applied mathematics #Square matrix #Polar #Pure mathematics
- When is a matrix a difference of two idempotents
1990/03/01 by Robert E. Hartwig, Mohan S. Putcha · 6 citations
Computer Science · Engineering · Mathematics · #Advanced Topics in Algebra #Algebra over a field #Arithmetic #Artificial intelligence #Block (permutation group theory) #Combinatorics #Computer science #Divisor (algebraic geometry) #Image (mathematics) #Involutory matrix #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Pure mathematics #Similarity (geometry) #Square matrix #Symmetric matrix #graph theory and CDMA systems
- A Complex Orthogonal-Symmetric Analog of the Polar Decomposition
1987/04/01 by Dipa Choudhury, Roger A. Horn · 2 citations
Computer Science · Engineering · Mathematics · #Matrix Theory and Algorithms #graph theory and CDMA systems #Advanced Topics in Algebra #Mathematics #Invertible matrix #Polar decomposition #Hermitian matrix #Factorization #Unitary state #Pure mathematics #Square (algebra) #Triple system #Square matrix #Combinatorics #Symmetric matrix #Polar #Algebra over a field #Algorithm #Geometry
- Newton's Method for the Matrix Square Root
1986/04/01 by Nicholas J. Higham · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Eigenvalues and eigenvectors #Geometry #Iterative Methods for Nonlinear Equations #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Newton's method #Nonlinear system #Root (linguistics) #Scientific Research and Discoveries #Square matrix #Square root #Symmetric matrix
- A trace inequality for M-matrices and the symmetrizability of a real matrix by a positive diagonal matrix
1985/11/01 by Miroslav Fiedler, Charles R. Johnson, Thomas L. Markham +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Topics in Algebra #Band matrix #Block matrix #Combinatorics #Diagonal #Diagonal matrix #Diagonally dominant matrix #Eigenvalues and eigenvectors #Geometry #Invertible matrix #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Nonnegative matrix #Physics #Pure mathematics #Square matrix #Symmetric matrix #TRACE (psycholinguistics) #graph theory and CDMA systems
- A Drazin inverse for rectangular matrices
1980/02/01 by Randall E. Cline, T.N.E. Greville, T. N. E. Greville · 5 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Advanced Optimization Algorithms Research #Chemistry #Combinatorics #Complex matrix #Drazin inverse #Eigenvalues and eigenvectors #Electromagnetic Scattering and Analysis #Geometry #Integer (computer science) #Inverse #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Physics #Pure mathematics #Square (algebra) #Square matrix #Symmetric matrix
- The matrix sign function and computations in systems
1976/01/01 by Eugene D. Denman, Alex N. Beavers · 5 citations
Computer Science · Mathematics · #Algebraic Riccati equation #Algebraic equation #Applied mathematics #Coefficient matrix #Differential equation #Eigendecomposition of a matrix #Eigenvalues and eigenvectors #Function (biology) #Generalized eigenvector #Lyapunov equation #Lyapunov function #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix decomposition #Matrix differential equation #Matrix function #Nonnegative matrix #Numerical methods for differential equations #Riccati equation #Sign (mathematics) #Sign function #Square matrix #State-transition matrix #Symmetric matrix
- XV. On systems of linear indeterminate equations and congruences
1861/12/31 by Henry J. Stephen Smith · 6 citations
Mathematics · Chemistry · #History and Theory of Mathematics #Mathematics #Square matrix #Matrix (chemical analysis) #Symbol (formal) #Type (biology) #Square (algebra) #Combinatorics #Congruence relation #Pure mathematics #Order (exchange) #Symmetric matrix #Physics #Eigenvalues and eigenvectors #Geometry #Computer science #Quantum mechanics #Chemistry