Multiple search direction conjugate gradient method II: theory and numerical experiments

DOI10.1080/00207160412331289065zbMath1067.65031OpenAlexW2072004616MaRDI QIDQ4652749

Xuebin Chi, Xing-Ping Liu, Tong-Xiang Gu, Ze-Yao Mo

Publication date: 28 February 2005

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160412331289065

zbMATH Keywords

consistencyconvergence accelerationnumerical experimentspreconditioningsteepest descent methodmassively parallel computingconjugate gradient-type methodChebyshev semi-iterative accelerationglobal inner product free-conjugate gradient methodsmultiple search direction conjugate gradient methodnonstationary Richardson iterative methodsecond order nonlinear nonsteady diffusion equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Iterative numerical methods for linear systems (65F10) Numerical computation of matrix norms, conditioning, scaling (65F35) Parallel numerical computation (65Y05)

Related Items

Minimizing synchronizations in sparse iterative solvers for distributed supercomputers ⋮ A parallel version of GPBi-CG method suitable for distributed parallel computing ⋮ A cooperative conjugate gradient method for linear systems permitting efficient multi-thread implementation ⋮ An improved parallel hybrid bi-conjugate gradient method suitable for distributed parallel computing

Cites Work

• Unnamed Item
• Multitasking the conjugate gradient method on the CRAY X-MP/48
• A performance model for Krylov subspace methods on mesh-based parallel computers
• The block preconditioned conjugate gradient method on vector computers
• s-step iterative methods for symmetric linear systems
• Parallel conjugate gradient-like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor
• The block conjugate gradient algorithm and related methods
• Conjugate gradient and Lanczos methods for sparse matrices on distributed memory multiprocessors
• Preconditioned CG methods for sparse matrices on massively parallel machines
• Krylov Subspace Methods on Supercomputers
• A Black Box Generalized Conjugate Gradient Solver with Inner Iterations and Variable-Step Preconditioning
• Generalized Schwarz Splittings
• Iterative Methods by Space Decomposition and Subspace Correction
• Optimizing a Parallel Conjugate Gradient Solver