Krylov subspace methods for functions of fractional differential operators

2018 ◽  
Vol 88 (315) ◽  
pp. 293-312 ◽  
Author(s):  
Igor Moret ◽  
Paolo Novati
Keyword(s):  
Krylov Subspace ◽  
Differential Operators ◽  
Krylov Subspace Methods ◽  
Subspace Methods ◽  
Fractional Differential ◽  
Fractional Differential Operators

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 Local Fractional Fourier Series with Application to Wave Equation in Fractal Vibrating String

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Ming-Sheng Hu ◽  
Ravi P. Agarwal ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Series Solution ◽  
Differential Operators ◽  
Fractional Wave Equation ◽  
Local Fractional Calculus ◽  
Vibrating String ◽  
Fractional Differential ◽  
Fractional Differential Operators

We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag-Leffler function.

POWER GRIDS ANALYSIS IN COMPRESSED KRYLOV-SUBSPACE METHODS

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.

scholarly journals Spectral Approximation of Fractional PDEs in Image Processing and Phase Field Modeling

2017 ◽  
Vol 17 (4) ◽  
pp. 661-678 ◽  
Author(s):  
Harbir Antil ◽  
Sören Bartels
Keyword(s):  
Image Processing ◽  
Phase Field ◽  
Differential Operators ◽  
Mathematical Tool ◽  
Phase Field Models ◽  
Field Modeling ◽  
Regularity Properties ◽  
Fractional Pdes ◽  
Fractional Differential ◽  
Fractional Differential Operators

AbstractFractional differential operators provide an attractive mathematical tool to model effects with limited regularity properties. Particular examples are image processing and phase field models in which jumps across lower dimensional subsets and sharp transitions across interfaces are of interest. The numerical solution of corresponding model problems via a spectral method is analyzed. Its efficiency and features of the model problems are illustrated by numerical experiments.

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