Mixed-Precision Cholesky QR Factorization and Its Case Studies on Multicore CPU with Multiple GPUs

DOI10.1137/14M0973773zbMath1320.65046OpenAlexW1558296484MaRDI QIDQ5254777

Ichitaro Yamazaki, Stanimire Z. Tomov, Jack J. Dongarra

Publication date: 10 June 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/14m0973773

zbMATH Keywords

orthogonalizationGPU computationmixed-precision

Mathematics Subject Classification ID

Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05) Orthogonalization in numerical linear algebra (65F25) Numerical algorithms for specific classes of architectures (65Y10)

Related Items

Mixed precision algorithms in numerical linear algebra, Randomized algorithms for distributed computation of principal component analysis and singular value decomposition, Mixed-precision explicit stabilized Runge-Kutta methods for single- and multi-scale differential equations, Floating-point arithmetic, Householder Orthogonalization with a Nonstandard Inner Product, A mixed precision LOBPCG algorithm, Cholesky and Gram-Schmidt Orthogonalization for Tall-and-Skinny QR Factorizations on Graphics Processors, Mixed precision bisection, Linear algebra software for large-scale accelerated multicore computing, The Stability of Block Variants of Classical Gram--Schmidt, Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices, Randomized GPU Algorithms for the Construction of Hierarchical Matrices from Matrix-Vector Operations, Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects, Block Gram-Schmidt algorithms and their stability properties, Scalable Linear Solvers Based on Enlarged Krylov Subspaces with Dynamic Reduction of Search Directions, Block Modified Gram--Schmidt Algorithms and Their Analysis, Mixed-Precision Cholesky QR Factorization and Its Case Studies on Multicore CPU with Multiple GPUs, Exploiting Lower Precision Arithmetic in Solving Symmetric Positive Definite Linear Systems and Least Squares Problems, PACF: a precision-adjustable computational framework for solving singular values

Uses Software

• LBNL
• CholQR

Cites Work

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• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• Iterative algorithms for Gram-Schmidt orthogonalization
• Reorthogonalized block classical Gram-Schmidt
• Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
• Communication-optimal Parallel and Sequential QR and LU Factorizations
• Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method
• Numerical Methods for Large Eigenvalue Problems
• Computing and Deflating Eigenvalues While Solving Multiple Right-Hand Side Linear Systems with an Application to Quantum Chromodynamics
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A Newton basis GMRES implementation
• A Block Orthogonalization Procedure with Constant Synchronization Requirements
• Iterative Krylov Methods for Large Linear Systems
• Mixed-Precision Cholesky QR Factorization and Its Case Studies on Multicore CPU with Multiple GPUs
• Solving linear least squares problems by Gram-Schmidt orthogonalization