On the Complexity of the Preconditioned Conjugate Gradient Algorithm for Solving Toeplitz Systems with a Fisher--Hartwig Singularity

Yi Lu; Clifford M. Hurvich

doi:10.1137/040612117

On the Complexity of the Preconditioned Conjugate Gradient Algorithm for Solving Toeplitz Systems with a Fisher--Hartwig Singularity

SIAM Journal on Matrix Analysis and Applications ◽

10.1137/040612117 ◽

2005 ◽

Vol 27 (3) ◽

pp. 638-653 ◽

Cited By ~ 8

Author(s):

Yi Lu ◽

Clifford M. Hurvich

Keyword(s):

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient ◽

Toeplitz Systems

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A modified scaled memoryless BFGS preconditioned conjugate gradient algorithm for nonsmooth convex optimization

Journal of Industrial & Management Optimization ◽

10.3934/jimo.2017075 ◽

2018 ◽

Vol 14 (2) ◽

pp. 785-801

Author(s):

Yigui Ou ◽

◽

Xin Zhou

Keyword(s):

Convex Optimization ◽

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient ◽

Nonsmooth Convex Optimization

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Parallel Preconditioned Conjugate Gradient Algorithm on GPU

Computational Methods for Engineering Technology ◽

10.4203/csets.34.9 ◽

2015 ◽

pp. 209-225

Author(s):

F. Andzembe ◽

J. Koko

Keyword(s):

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient

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A preconditioned conjugate gradient algorithm for GeneRank with application to microarray data mining

Data Mining and Knowledge Discovery ◽

10.1007/s10618-011-0245-7 ◽

2011 ◽

Vol 26 (1) ◽

pp. 27-56 ◽

Cited By ~ 8

Author(s):

Gang Wu ◽

Wei Xu ◽

Ying Zhang ◽

Yimin Wei

Keyword(s):

Data Mining ◽

Microarray Data ◽

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient

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Evaluation of a preconditioned conjugate-gradient algorithm for weighted least-squares unwrapping of digital speckle-pattern interferometry phase maps

Applied Optics ◽

10.1364/ao.37.003076 ◽

1998 ◽

Vol 37 (14) ◽

pp. 3076 ◽

Cited By ~ 33

Author(s):

Guillermo H. Kaufmann ◽

Gustavo E. Galizzi ◽

Pablo D. Ruiz

Keyword(s):

Least Squares ◽

Conjugate Gradient ◽

Speckle Pattern ◽

Weighted Least Squares ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient ◽

Digital Speckle Pattern Interferometry ◽

Digital Speckle

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Fast optimal wavefront reconstruction for multi-conjugate adaptive optics using the Fourier domain preconditioned conjugate gradient algorithm

Optics Express ◽

10.1364/oe.14.007487 ◽

2006 ◽

Vol 14 (17) ◽

pp. 7487 ◽

Cited By ~ 24

Author(s):

Curtis R. Vogel ◽

Qiang Yang

Keyword(s):

Adaptive Optics ◽

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient ◽

Fourier Domain ◽

Wavefront Reconstruction

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A multi-GPU parallel optimization model for the preconditioned conjugate gradient algorithm

Parallel Computing ◽

10.1016/j.parco.2017.04.003 ◽

2017 ◽

Vol 63 ◽

pp. 1-16 ◽

Cited By ~ 10

Author(s):

Jiaquan Gao ◽

Yuanshen Zhou ◽

Guixia He ◽

Yifei Xia

Keyword(s):

Conjugate Gradient ◽

Optimization Model ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Parallel Optimization ◽

Preconditioned Conjugate Gradient

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Scaled memoryless BFGS preconditioned conjugate gradient algorithm for unconstrained optimization

Optimization Methods and Software ◽

10.1080/10556780600822260 ◽

2007 ◽

Vol 22 (4) ◽

pp. 561-571 ◽

Cited By ~ 45

Author(s):

Neculai Andrei

Keyword(s):

Unconstrained Optimization ◽

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient

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Parallelizing the Conjugate Gradient Algorithm for Multilevel Toeplitz Systems

Procedia Computer Science ◽

10.1016/j.procs.2013.05.221 ◽

2013 ◽

Vol 18 ◽

pp. 571-580 ◽

Cited By ~ 4

Author(s):

Jie Chen ◽

Tom L.H. Li

Keyword(s):

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Toeplitz Systems

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SSOR Preconditioned Conjugate Gradient Algorithm in Dynamic SMP Clusters with Communication on the Fly

The 4th International Symposium on Parallel and Distributed Computing (ISPDC'05) ◽

10.1109/ispdc.2005.44 ◽

2006 ◽

Author(s):

Marek Tudruj Boguslaw Butrylo

Keyword(s):

Conjugate Gradient ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient ◽

Smp Clusters

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Application of the preconditioned conjugate-gradient algorithm to the integral equations for microwave circuits

Microwave and Optical Technology Letters ◽

10.1002/mop.10434 ◽

2002 ◽

Vol 34 (4) ◽

pp. 266-270 ◽

Cited By ~ 2

Author(s):

K. F. Tsang ◽

R. S. Chen ◽

Mo Lei ◽

Edward K. N. Yung

Keyword(s):

Integral Equations ◽

Conjugate Gradient ◽

Microwave Circuits ◽

Conjugate Gradient Algorithm ◽

Gradient Algorithm ◽

Preconditioned Conjugate Gradient

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