Preconditioned Krylov Subspace Methods for the Numerical Solution of Markov Chains

AbstractThe Krylov subspace method has been investigated and refined for approximating the behaviors of finite or infinite dimensional linear operators. It has been used for approximating eigenvalues, solutions of linear equations, and operator functions acting on vectors. Recently, for time-series data analysis, much attention is being paid to the Krylov subspace method as a viable method for estimating the multiplications of a vector by an unknown linear operator referred to as a transfer operator. In this paper, we investigate a convergence analysis for Krylov subspace methods for estimating operator-vector multiplications.

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Tensor Krylov subspace methods with an invertible linear transform product applied to image processing

Applied Numerical Mathematics ◽

10.1016/j.apnum.2021.04.007 ◽

2021 ◽

Vol 166 ◽

pp. 186-207

Author(s):

Lothar Reichel ◽

Ugochukwu O. Ugwu

Keyword(s):

Image Processing ◽

Krylov Subspace ◽

Krylov Subspace Methods ◽

Subspace Methods ◽

Linear Transform

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Waveform Krylov subspace methods for tightly coupled systems

1996 IEEE International Symposium on Circuits and Systems. Circuits and Systems Connecting the World. ISCAS 96 ◽

10.1109/iscas.1996.542019 ◽

2002 ◽

Author(s):

Wai-Shing Luk ◽

O. Wing

Keyword(s):

Krylov Subspace ◽

Krylov Subspace Methods ◽

Coupled Systems ◽

Subspace Methods ◽

Tightly Coupled ◽

Tightly Coupled Systems

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Krylov Subspace Methods in Dynamical Sampling

Sampling Theory, Signal Processing, and Data Analysis ◽

10.1007/bf03549595 ◽

2016 ◽

Vol 15 (1) ◽

pp. 9-20

Author(s):

Akram Aldroubi ◽

Ilya Krishtal

Keyword(s):

Krylov Subspace ◽

Krylov Subspace Methods ◽

Subspace Methods

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POWER GRIDS ANALYSIS IN COMPRESSED KRYLOV-SUBSPACE METHODS

Journal of Circuits System and Computers ◽

10.1142/s0218126608004435 ◽

2008 ◽

Vol 17 (03) ◽

pp. 439-446

Author(s):

HAOHANG SU ◽

YIMEN ZHANG ◽

YUMING ZHANG ◽

JINCAI MAN

Keyword(s):

Present Method ◽

Large Scale ◽

Krylov Subspace ◽

Power Grid ◽

Excellent Result ◽

Krylov Subspace Methods ◽

Power Grids ◽

Improved Method ◽

Subspace Methods ◽

Transient Simulations

An improved method is proposed based on compressed and Krylov-subspace iterative approaches to perform efficient static and transient simulations for large-scale power grid circuits. It is implemented with CG and BiCGStab algorithms and an excellent result has been obtained. Extensive experimental results on large-scale power grid circuits show that the present method is over 200 times faster than SPICE3 and around 10–20 times faster than ICCG method in transient simulations. Furthermore, the presented algorithm saves the memory usage over 95% of SPICE3 and 75% of ICCG method, respectively while the accuracy is not compromised.

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