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Practical Implementation of Krylov Subspace Spectral Methods
Journal of Scientific Computing, 2007Krylov subspace spectral methods have been shown to be high-order accurate in time and more stable than time-stepping methods but also more difficult for an efficient implementation. The author shows how these methods should be used in practical solvers by exploiting the simple structure of differential operators.
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A Krylov subspace method for large estimation problems
1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258), 1999Computing the linear least-squares estimate of a high-dimensional random quantity given noisy data requires solving a large system of linear equations. In many situations, one can solve this system efficiently using the conjugate gradient (CG) algorithm. Computing the estimation error variances is a more intricate task.
Michael K. Schneider, Alan S. Willsky
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On Coarse Grid Correction Methods in Krylov Subspaces
Journal of Mathematical Sciences, 2018The authors consider the numerical solution of large, sparse, and ill-conditioned systems of linear algebraic equations (SLAEs) originated from a boundary value problem with Dirichlet boundary conditions for a convection-diffusion equation based on a finite volume method of second order derived by the second author [J. Math. Sci., New York 224, No.
Gurieva, Y. L., Il'in, V. P.
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Truncation Strategies for Optimal Krylov Subspace Methods
SIAM Journal on Numerical Analysis, 1999Summary: Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal basis for the entire Krylov subspace to compute the minimal residual approximation to the solution. Therefore, when the number of iterations becomes large, the amount of work and the storage requirements become excessive. In practice one has to limit the resources.
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The Origin and Development of Krylov Subspace Methods
Computing in Science & Engineering, 2022openaire +1 more source
Inexact rational Krylov subspace method for eigenvalue problems
Numerical Linear Algebra With Applications, 2022Shengjie Xu
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3D large-scale transient electromagnetic modeling using a Shift-and-Invert Krylov subspace method
Journal of Applied Geophysics, 2022Kailiang Lu, Jianmei Zhou, Xiu Li
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