Krylov Subspace Method Using Quantum Computing

2021 ◽  
pp. 271-279
Author(s):  
Vidushi Jain ◽  
Yogesh Nagor
Keyword(s):  
Quantum Computing ◽  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Subspace Method

scholarly journals Krylov subspace methods for estimating operator-vector multiplications in Hilbert spaces

2021 ◽  
Author(s):  
Yuka Hashimoto ◽  
Takashi Nodera
Keyword(s):  
Krylov Subspace ◽  
Time Series Data ◽  
Linear Equations ◽  
Transfer Operator ◽  
Krylov Subspace Methods ◽  
Krylov Subspace Method ◽  
Linear Operators ◽  
Series Data ◽  
Subspace Method ◽  
Subspace Methods

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.

scholarly journals Preconditioned Krylov subspace method for the solution of least-squares problems

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2020151-2020152 ◽  
Author(s):  
jun-Feng Yin ◽  
Ken Hayami ◽  
Zhong-Zhi Bai
Keyword(s):  
Least Squares ◽  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Subspace Method ◽  
Least Squares Problems ◽  
Preconditioned Krylov Subspace Method

Fast EM Stress Evolution Analysis Using Krylov Subspace Method

2019 ◽  
pp. 47-66
Author(s):  
Sheldon Tan ◽  
Mehdi Tahoori ◽  
Taeyoung Kim ◽  
Shengcheng Wang ◽  
Zeyu Sun ◽  
...  
Keyword(s):  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Subspace Method ◽  
Stress Evolution ◽  
Evolution Analysis

Refined Algorithm for Solving High-Order Harmonics of Multi Group Neutron Diffusion Equation

2017 ◽  
Author(s):  
Gaoxin Zhou ◽  
Zhi Gang
Keyword(s):  
Diffusion Equation ◽  
Iteration Method ◽  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Neutron Diffusion ◽  
Subspace Method ◽  
Arnoldi Method ◽  
Arnoldi Algorithm ◽  
Eigenvalue And Eigenvector ◽  
Neutron Diffusion Equation

In recent years, high order harmonic (or eigenvector) of neutron diffusion equation has been widely used in on-line monitoring system of reactor power. There are two kinds of calculation method to solve the equation: corrected power iteration method and Krylov subspace methods. Fu Li used the corrected power iteration method. When solving for the ith harmonic, it tries to eliminate the influence of the front harmonics using the orthogonality of the harmonic function. But its convergence speed depends on the occupation ratio. When the dominant ratios equal to 1 or close to 1, convergence speed of fixed source iteration method is slow or convergence can’t be achieved. Another method is the Krylov subspace method, the main idea of this method is to project the eigenvalue and eigenvector of large-scale matrix to a small one. Then we can solve the small matrix eigenvalue and eigenvector to get the large ones. In recent years, the restart Arnoldi method emerged as a development of Krylov subspace method. The method uses continuous reboot Arnoldi decomposition, limiting expanding subspace, and the orthogonality of the subspace is guaranteed using orthogonalization method. This paper studied the refined algorithms, a method based on the Krylov subspace method of solving eigenvalue problem for large sparse matrix of neutron diffusion equation. Two improvements have been made for a restarted Arnoldi method. One is that using an ingenious linear combination of the refined Ritz vector forms an initial vector and then generates a new Krylov subspace. Another is that retaining the refined Ritz vector in the new subspace, called, augmented Krylov subspace. This way retains useful information and makes the resulting algorithm converge faster. Several numerical examples are the new algorithm with the implicitly restart Arnoldi algorithm (IRA) and the implicitly restarted refined Arnoldi algorithm (IRRA). Numerical results confirm efficiency of the new algorithm.

3-D Full-Time TEM Modeling Using Shift-and-Invert Krylov Subspace Method

2020 ◽  
Vol 58 (10) ◽  
pp. 7096-7104
Author(s):  
Jianmei Zhou ◽  
Wentao Liu ◽  
Xiu Li ◽  
Yanfu Qi ◽  
Zhipeng Qi
Keyword(s):  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Full Time ◽  
Subspace Method

Performance of Krylov subspace method with SOR preconditioner supported by Eisenstat’s technique for linear system derived from time-periodic FEM

2019 ◽  
Vol 38 (5) ◽  
pp. 1641-1654 ◽  
Author(s):  
Makoto Kumagai ◽  
Shimpei Kakita ◽  
Yoshifumi Okamoto
Keyword(s):  
Linear System ◽  
Iterative Process ◽  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Subspace Method ◽  
Linear Solvers ◽  
Content Type ◽  
Type Reactor ◽  
Three Phase ◽  
Time Periodic

Purpose This paper aims to present the affinity of BiCGStab and BiCGStab2 with successive over-relaxation (SOR) preconditioner supported by Eisenstat’s technique for a linear system derived from the time-periodic finite element method (TP-FEM). To solve the time domain electromagnetic field problem with long transient state, TP-FEM is very useful from the perspective of rapidly achieving a steady state. Because TP-FEM solves all of the state variables at once, the linear system derived from TP-FEM becomes the large scale and nonsymmetric, whereas the detailed performance of some preconditioned Krylov subspace method is not reported. Design/methodology/approach In this paper, BiCGStab and BiCGStab2 are used as the linear solver for a large-sparse nonsymmetric linear system derived from TP-FEM. In addition, incomplete LU (ILU) factorization is applied as a preconditioner to compare SOR supported by Eisenstat’s technique. As examples, the pot-type reactor and three-phase transformer is analyzed. Findings In the problem of the pot-type reactor, when SOR preconditioner supported by Eisenstat’s technique is applied to BiCGStab and BiCGStab2, the elapsed time can be reduced dramatically. However, in the problem of the three-phase transformer, the iterative process of the linear solvers with SOR preconditioner is not terminated, whereas the iterative process of linear solvers with ILU preconditioner is terminated. The preconditioner that can be supported by Eisenstat’s technique is not necessarily appropriate for the problem to derive from TP-FEM. Originality/value In this paper, the affinity of preconditioned linear solver supported by Eisenstat’s technique for the nonsymmetric linear system derived from TP-FEM is demonstrated.

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