The conjugate-gradient method for solving linear systems

Hestenes, Magnus R.

doi:10.1090/psapm/006/0084178

Cited by 181 publications

(168 citation statements)

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“…Thus, this caveat limits its application. To overcome this limitation, iterative methods such as the conjugate gradient method (CGM) [10] or the more advanced CG-FFT method and its various forms [11] have been applied. These methods reduce the computation time and memory requirements significantly.…”

Section: Cg-fft Solution Techniquementioning

confidence: 99%

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Computation of Electromagnetic Fields inside Three Dimensional Inhomogeneous Dielectrics Using a Buffered Block Forward Backward Algorithm

Condon

Babu

2006

2006 7th International Symposium on Antennas, Propagation &Amp; EM Theory

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Abstract:The paper is concerned with the electromagnetic scattering from a three-dimensional inhomogeneous dielectric object. In particular, the paper compares the use of a Buffered Block Forward Backward (BBFB) algorithm to the use of the commonly employed weak form of the CG-FFT method for the numerical solution of the resultant Electric Field Integral Equation (EFIE). The BBFB method is based on the spatial segmentation of the dielectric into smaller pieces. Results are shown which illustrate the convergence of the algorithm and its superior performance to the CG-FFT.

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Section: Cg-fft Solution Techniquementioning

confidence: 99%

“…j=i+l,job(i) (10) Liidi(k+l) =e-ZLijdj(k)-ZLijdi(k+1) (11) While the quantity db(i) is redundant, the minimal amount of increased computational overload results in an accurate algorithm and a far faster level of convergence. Each sweep of the BBFB is solved using the CG method.…”

Section: Buffered Block Forward Backward (Bbfb)mentioning

confidence: 99%

Computation of Electromagnetic Fields inside Three Dimensional Inhomogeneous Dielectrics Using a Buffered Block Forward Backward Algorithm

Condon

Babu

2006

2006 7th International Symposium on Antennas, Propagation &Amp; EM Theory

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“…For nonlinear conjugate gradient methods .The extension of the conjugacy condition was studied by Perry [10], he tried to accelerate the conjugate gradient method by incorporating the second-order information into it specifically, he used the secant condition Holds By taking this relation into account, Perry replaced the conjugacy condition (1.8) by the condition…”

Section: Introductionmentioning

confidence: 99%

New Three-Term Conjugate Gradient Method for Solving Unconstrained Optimization Problems

Linda¹

2017

IJMCAR

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“…The FR method [9], the PRP method [17,18], the HS method [12] and the DY method [7] are several famous formulas and regarded as the four leading conjugate gradient methods [16]. They are specified by…”

Section: Introductionmentioning

confidence: 99%

A Globally and R-Linearly Convergent Hybrid HS and PRP Method and its Inexact Version with Applications

Zhou

2015

Ukr Math J

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A hybrid HS and PRP type conjugate gradient method for smooth optimization is presented, which reduces to the classical RPR or HS method if exact linear search is used and converges globally and R-linearly for nonconvex functions with an inexact backtracking line search under standard assumption. An inexact version of the proposed method which admits possible approximate gradient or/and approximate function values is also given. It is very important for such problems whose gradients or function values are not available or difficult to compute. The inexact version is proved to be globally convergent for general functions using some approximate descent line search. Moreover, the inexact method is applied to solve a nonsmooth convex optimization problem by converting it into a once continuously differentiable function by way of the Moreau-Yosida regularization.

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The conjugate-gradient method for solving linear systems

Cited by 181 publications

References 0 publications

Computation of Electromagnetic Fields inside Three Dimensional Inhomogeneous Dielectrics Using a Buffered Block Forward Backward Algorithm

Computation of Electromagnetic Fields inside Three Dimensional Inhomogeneous Dielectrics Using a Buffered Block Forward Backward Algorithm

New Three-Term Conjugate Gradient Method for Solving Unconstrained Optimization Problems

A Globally and R-Linearly Convergent Hybrid HS and PRP Method and its Inexact Version with Applications

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