• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.3
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• pp.371-383
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• 1999

An efficient and numerically stable eigensolution method for structures with multiple natural frequencies is presented. The proposed method is developed by improving the well-known subspace iteration method with shift. A major difficulty of the subspace iteration method with shift is that because of singularity problem, a shift close to an eigenvalue can not be used, resulting in slower convergence. In this paper, the above singularity problem has been solved by introducing side conditions without sacrifice of convergence. The proposed method is always nonsingular even if a shift is on a distinct eigenvalue or multiple ones. This is one of the significant characteristics of the proposed method. The nonsingularity is proved analytically. The convergence of the proposed method is at least equal to that of the subspace iteration method with shift, and the operation counts of above two methods are almost the same when a large number of eigenpairs are required. To show the effectiveness of the proposed method, two numerical examples are considered.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.39A no.10
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• pp.585-592
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• 2014

It is well known that serial belief propagation (BP) decoding for low-density parity-check (LDPC) codes achieves faster convergence without any increase of decoding complexity per iteration and bit error rate (BER) performance loss than standard parallel BP (PBP) decoding. Serial BP (SBP) decoding, such as horizontal SBP (H-SBP) decoding or vertical SBP (V-SBP) decoding, updates check nodes or variable nodes faster than standard PBP decoding within a single iteration. In this paper, we propose combined horizontal-vertical SBP (CHV-SBP) decoding. By the same reasoning, CHV-SBP decoding updates check nodes or variable nodes faster than SBP decoding within a serialized step in an iteration. CHV-SBP decoding achieves faster convergence than H-SBP or V-SBP decoding. We compare these decoding schemes in details. We also show in simulations that the convergence rate, in iterations, for CHV-SBP decoding is about $\frac{1}{6}$ of that for standard PBP decoding, while the convergence rate for SBP decoding is about $\frac{1}{2}$ of that for standard PBP decoding. In simulations, we use recently proposed generalized LDPC (GLDPC) codes with binary cyclic codes (BCC).

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.1 s.94
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• pp.112-117
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• 2005

Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in order to accelerate the convergence of the subspace iteration method. Proposed methods are divided into two forms according to the number of starting vectors. The first method composes 2p starting vectors when the number of required modes is p and the second method uses 1.5p starting vectors. To investigate the efficiency of proposed methods, two numerical examples are presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.717-720
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• 2004

Two modified versions of subspace iteration method using accelerated starting vectors are proposed to efficiently calculate free vibration modes of structures. Proposed methods employ accelerated Lanczos vectors as starting iteration vectors in the subspace iteration method. To investigate the efficiency of proposed methods, two numerical examples are presented.

• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.1095-1099
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• 2017

A fission source can act as a stabilization element in coupled Monte Carlo simulations. We have observed this while studying numerical instabilities in nonlinear steady-state simulations performed by a Monte Carlo criticality solver that is coupled to a xenon feedback solver via fixed-point iteration. While fixed-point iteration is known to be numerically unstable for some problems, resulting in large spatial oscillations of the neutron flux distribution, we show that it is possible to stabilize it by reducing the number of Monte Carlo criticality cycles simulated within each iteration step. While global convergence is ensured, development of any possible numerical instability is prevented by not allowing the fission source to converge fully within a single iteration step, which is achieved by setting a small number of criticality cycles per iteration step. Moreover, under these conditions, the fission source may converge even faster than in criticality calculations with no feedback, as we demonstrate in our numerical test simulations.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.869-885
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• 2021

In this article, we define Picard's three-step iteration process for the approximation of fixed points of Zamfirescu operators in an arbitrary Banach space. We prove a convergence result for Zamfirescu operator using the proposed iteration process. Further, we prove that Picard's three-step iteration process is almost T-stable and converges faster than all the known and leading iteration processes. To support our results, we furnish an illustrative numerical example. Finally, we apply the proposed iteration process to approximate the solution of a mixed Volterra-Fredholm functional nonlinear integral equation.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.667-678
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• 2015

The aim of this paper is to prove strong convergence theorem by a modified three step iterative process with errors for three nonexpansive mappings in the frame work of uniformly smooth Banach spaces. The main feature of this scheme is that its special cases can handle both strong convergence like Halpern type and weak convergence like Ishikawa type iteration schemes. Our result extend and generalize the result of S. H. Khan, Kim and Xu and many other authors.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1275-1284
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• 2001

In this paper, we introduce an iteration generated by countable nonexpansive mappings and prove a weak convergence theorem which is connected with the feasibility problem. This result is used to solve the problem of finding a solution of the countable convex inequality system and the problem of finding a common fixed point for a commuting countable family of nonexpansive mappings.

• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.341-378
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• 1997

We consider three classes of numerical methods for solv-ing the semi-explicit differential-algebraic equations of index 1 and higher. These methods use implicit multistep fixed stepsize methods and several iterative processes including simple iteration, full a2nd modified Newton iteration. For these methods we prove convergence theorems and derive error estimates. We consider different ways of choosing initial approximations for these iterative methods and in-vestigate their efficiency in theory and practice.

• East Asian mathematical journal
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• v.28 no.1
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• pp.81-92
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• 2012

The purpose of this paper is to establish strong convergence of an implicit iteration process to a common fixed point for a finite family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. Our results improve and extend the corresponding results of Fukhar-ud-din et al. [15] and some others from the current literature.