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Block Preconditioning for the Conjugate Gradient Method [PDF]
SIAM Journal on Scientific and Statistical Computing, 1985 Different block preconditionings for the conjugate gradient methods are investigated for solving positive definite block tridiagonal systems. These preconditionings are based on different sparse approximate matrix inverses. The proposed methods are compared with other well-known preconditionings as for example the point incomplete Cholesky ...
Concus, P., Golub, G.H., Meurant, G.
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An inexact Newton method with inner preconditioned CG for non-uniformly monotone elliptic problems
Mathematical Modelling and Analysis, 2021 The present paper introduces an inexact Newton method, coupled with a preconditioned conjugate gradient method in inner iterations, for elliptic operators with non-uniformly monotone upper and lower bounds.
Benjámin Borsos
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A new preconditioned conjugate gradient power flow [PDF]
IEEE Transactions on Power Systems, 2002 A new solution methodology for the constant matrix, decoupled power flow problem is presented in this paper. The proposed method uses the conjugate gradient method instead of the traditional direct solution of Ax = b for updating the power flow variables.
H. Dag, A. Semlyen
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Mathematics, 2022 This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the ...
Tao Li, Qing-Wen Wang, Xin-Fang Zhang
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A PCG ALGORITHM FOR NON-LINEAR OPTIMIZATION BASED ON A QUADRATIC MODEL [PDF]
مجلة التربية والعلم, 2006 In this paper a new preconditioned Extended Conjugate Gradient with self-scaling Variable Metric method is proposed for unconstrained optimization. This method is based on the inexact line searches and it is examined by using different nonlinear test ...
Abbas. AI-Bayati +1 more
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About analysis of large problems of structural mechanics on multi-core computers [PDF]
Инженерно-строительный журнал, 2013 The sparse direct solvers as well as iterative methods are considered for analysis of large-scale finite element problems of structural mechanics on multi-core computers.
S.Yu. Fialko
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Explicit conjugate gradient method with preconditioning [PDF]
Applications of Mathematics, 1994 The authors propose the matrix \(C = (I - \omega A)^{-1}\) as a preconditioner in the preconditioned conjugate gradient (PCCG) method for solving the system of algebraic equations \(Ax = b\). Convergence properties of this PCCG method are analyzed. Especially, a relation between the condition numbers of the matrices \(C^{-1} A\) and \(A\) is derived ...
Křížková, Jitka, Vaněk, Petr
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Fourier domain preconditioned conjugate gradient algorithm for atmospheric tomography [PDF]
, 2006 By 'atmospheric tomography' we mean the estimation of a layered atmospheric turbulence profile from measurements of the pupil-plane phase (or phase gradients) corresponding to several different guide star directions.
Ellerbroek, Brent L. +2 more
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Error Estimation in Preconditioned Conjugate Gradients
BIT Numerical Mathematics, 2005 The authors deal with the problem of convergence in the preconditioned conjugate gradient method for the solution of a linear system \(Ax=b\), where \(A\) is a symmetric positive definite \(n\times n\) matrix. Indeed, the problem of this convergence was the subject of many papers in literature.
Strakoš, Z. (Zdeněk) +1 more
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Shock and Vibration, 2021 The full-waveform inversion (FWI) of a Love wave has become a powerful tool for shallow-surface site characterization. In classic conjugate gradient algorithm- (CG) based FWI, the energy distribution of the gradient calculated with the adjoint state ...
Jianbo Guan, Yu Li, Guohua Liu
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