Linear algebra software for large-scale accelerated multicore computing
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Publication:5740076
DOI10.1017/S0962492916000015zbMath1353.65019OpenAlexW2407804532MaRDI QIDQ5740076
A. Haidar, Asim Yarkhan, Hartwig Anzt, Piotr Luszczek, Ahmad Abdelfattah, Mark Ralph Gates, Jakub Kurzak, Ichitaro Yamazaki, Stanimire Z. Tomov, Jack J. Dongarra
Publication date: 8 July 2016
Published in: Acta Numerica (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s0962492916000015
eigenproblemCholesky factorizationLU factorizationQR factorizationBLASsparse linear algebramulticore systemsLAPACKsingular value problemdistributed memory systemslinear algebra softwareLDLT decomposition
Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical solutions to overdetermined systems, pseudoinverses (65F20) Direct numerical methods for linear systems and matrix inversion (65F05) Packaged methods for numerical algorithms (65Y15)
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Uses Software
Cites Work
- Unnamed Item
- A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
- Accelerating the reduction to upper Hessenberg, tridiagonal, and bidiagonal forms through hybrid GPU-based computing
- Accelerating scientific computations with mixed precision algorithms
- Parallel two-stage reduction to Hessenberg form using dynamic scheduling on shared-memory architectures
- On parallelism and convergence of incomplete LU factorizations
- Efficient eigenvalue and singular value computations on shared memory machines
- Parallel algorithms for solving linear systems with sparse triangular matrices
- The effect of ordering on preconditioned conjugate gradients
- Multifrontal parallel distributed symmetric and unsymmetric solvers
- On asynchronous iterations
- Relaxation strategies for nested Krylov methods
- Block reduction of matrices to condensed forms for eigenvalue computations
- New insights in GMRES-like methods with variable preconditioners
- Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides
- Flexible Conjugate Gradients
- The Multishift QR Algorithm. Part I: Maintaining Well-Focused Shifts and Level 3 Performance
- The Multishift QR Algorithm. Part II: Aggressive Early Deflation
- Communication-optimal Parallel and Sequential QR and LU Factorizations
- Partitioned Triangular Tridiagonalization
- Aggregation Methods for Solving Sparse Triangular Systems on Multiprocessors
- Factors Impacting Performance of Multithreaded Sparse Triangular Solve
- Accelerating Linear System Solutions Using Randomization Techniques
- CALU: A Communication Optimal LU Factorization Algorithm
- Improving the Accuracy of Computed Singular Values
- Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine
- SOLVING SPARSE TRIANGULAR LINEAR SYSTEMS ON PARALLEL COMPUTERS
- Average-Case Stability of Gaussian Elimination
- Error bounds from extra-precise iterative refinement
- Using Mixed Precision for Sparse Matrix Computations to Enhance the Performance while Achieving 64-bit Accuracy
- Noise radiation from a ducted rotor in a swirling-translating flow
- Performance and Accuracy of LAPACK's Symmetric Tridiagonal Eigensolvers
- The Multifrontal Solution of Indefinite Sparse Symmetric Linear
- Improving the Accuracy of Computed Eigenvalues and Eigenvectors
- The WY Representation for Products of Householder Matrices
- An extended set of FORTRAN basic linear algebra subprograms
- Multicolor ICCG Methods for Vector Computers
- A Storage-Efficient $WY$ Representation for Products of Householder Transformations
- LAPACK Users' Guide
- Principal component analysis in linear systems: Controllability, observability, and model reduction
- A Vectorizable Variant of some ICCG Methods
- A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable-Step Preconditioning
- Stability of Methods for Matrix Inversion
- A Fast Reordering Algorithm for Parallel Sparse Triangular Solution
- Efficient High Accuracy Solutions with ${\text{GMRES}}(m)$
- Ill-Conditioned Eigensystems and the Computation of the Jordan Canonical Form
- Basic Linear Algebra Subprograms for Fortran Usage
- Accurate Symmetric Indefinite Linear Equation Solvers
- A Divide-and-Conquer Algorithm for the Bidiagonal SVD
- A set of level 3 basic linear algebra subprograms
- Locality of Reference in LU Decomposition with Partial Pivoting
- Algorithm 807
- Flexible Inner-Outer Krylov Subspace Methods
- Inexact Preconditioned Conjugate Gradient Method with Inner-Outer Iteration
- Scalable Parallel Preconditioning with the Sparse Approximate Inverse of Triangular Matrices
- Solving Sparse Linear Systems with Sparse Backward Error
- Accuracy and Stability of Numerical Algorithms
- GMRESR: a family of nested GMRES methods
- Historical Development of the Newton–Raphson Method
- Communication-Avoiding Symmetric-Indefinite Factorization
- Fine-Grained Parallel Incomplete LU Factorization
- Mixed-Precision Cholesky QR Factorization and Its Case Studies on Multicore CPU with Multiple GPUs
- Optimal Parallel Solution of Sparse Triangular Systems
- A Flexible Inner-Outer Preconditioned GMRES Algorithm
- Iterative Refinement in Floating Point
- A Numerical Method for Solving Fredholm Integral Equations of the First Kind Using Singular Values
- On the reduction of a symmetric matrix to tridiagonal form
