In this paper, we introduce some new iterative algorithms for the split common solution problems for equilibrium problems and fixed point problems of nonlinear mappings. Some examples illustrating our results are also...
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In this paper, we introduce some new iterative algorithms for the split common solution problems for equilibrium problems and fixed point problems of nonlinear mappings. Some examples illustrating our results are also given. MSC: 47J25, 47H09, 65K10.
Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of strictly p...
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Based on a viscosity hybrid steepest-descent method, in this paper, we introduce an iterative scheme for finding a common element of a system of equilibrium and fixed point problems of an infinite family of strictly pseudo-contractive mappings which solves the variational inequality <(gamma f - mu F)q, p - q > <= 0 for p epsilon boolean AND F-infinity(i=1)(T-i). Furthermore, we also prove the strong convergence theorems for the proposed iterative scheme and give a numerical example to support and illustrate our main theorem.
In this article, we introduce and study a new system of generalized quasi-variational-like inclusions with noncompact valued mappings. By using the eta-proximal mapping technique, we prove the existence of solutions a...
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In this article, we introduce and study a new system of generalized quasi-variational-like inclusions with noncompact valued mappings. By using the eta-proximal mapping technique, we prove the existence of solutions and the convergence of some new N-step iterative algorithms for this system of generalized quasi-variational-like inclusions. Our results extend and improve some known results in the literature. Mathematics Subject Classification 2000: 49H09;49J40;49H10.
A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) to compute the ...
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A new class of bilevel generalized mixed equilibrium problems involving set-valued mappings is introduced and studied in Banach spaces. First, an auxiliary generalized mixed equilibrium problem (AGMEP) to compute the approximate solutions of the generalized mixed equilibrium problems (GMEP) and bilevel generalized mixed equilibrium problems (BGMEP) involving set-valued mappings is introduced. By using a minimax inequality, the existence and uniqueness of solutions of the AGMEP is proved under quite mild conditions. By using auxiliary principle technique, new iterative algorithm to compute the approximate solutions of the GMEP and the BGMEP is suggested and analyzed. Strong convergence of the iterative sequences generated by the proposed algorithms is proved under quite mild assumptions. These results are new and generalize some recent results in this field.
Mammography is the primary imaging tool for screening and diagnosis of human breast cancers, but similar to 10-20% of palpable tumors are not detectable on mammograms and only about 40% of biopsied lesions are maligna...
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Mammography is the primary imaging tool for screening and diagnosis of human breast cancers, but similar to 10-20% of palpable tumors are not detectable on mammograms and only about 40% of biopsied lesions are malignant. Here we report a high-resolution, low-dose phase contrast X-ray tomographic method for 3D diagnosis of human breast cancers. By combining phase contrast X-ray imaging with an image reconstruction method known as equally sloped tomography, we imaged a human breast in three dimensions and identified a malignant cancer with a pixel size of 92 mu m and a radiation dose less than that of dual-view mammography. According to a blind evaluation by five independent radiologists, our method can reduce the radiation dose and acquisition time by similar to 74% relative to conventional phase contrast X-ray tomography, while maintaining high image resolution and image contrast. These results demonstrate that high-resolution 3D diagnostic imaging of human breast cancers can, in principle, be performed at clinical compatible doses.
Cloud computing, with its promise of virtually infinite resources, seems to suit well in solving resource greedy scientific computing problems. To study this, we established a scientific computing cloud (SciCloud) pro...
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Cloud computing, with its promise of virtually infinite resources, seems to suit well in solving resource greedy scientific computing problems. To study this, we established a scientific computing cloud (SciCloud) project and environment on our internal clusters. The main goal of the project is to study the scope of establishing private clouds at the universities. With these clouds, students and researchers can efficiently use the already existing resources of university computer networks, in solving computationally intensive scientific, mathematical, and academic problems. However, to be able to run the scientific computing applications on the cloud infrastructure, the applications must be reduced to frameworks that can successfully exploit the cloud resources, like the MapReduce framework. This paper summarizes the challenges associated with reducing iterative algorithms to the MapReduce model. algorithms used by scientific computing are divided into different classes by how they can be adapted to the MapReduce model;examples from each such class are reduced to the MapReduce model and their performance is measured and analyzed. The study mainly focuses on the Hadoop MapReduce framework but also compares it to an alternative MapReduce framework called Twister, which is specifically designed for iterative algorithms. The analysis shows that Hadoop MapReduce has significant trouble with iterative problems while it suits well for embarrassingly parallel problems, and that Twister can handle iterative problems much more efficiently. This work shows how to adapt algorithms from each class into the MapReduce model, what affects the efficiency and scalability of algorithms in each class and allows us to judge which framework is more efficient for each of them, by mapping the advantages and disadvantages of the two frameworks. This study is of significant importance for scientific computing as it often uses complex iterative methods to solve critical problems and adapting
in this paper, we introduce and study a new system of (A, eta)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A, eta)-accretive mappings, we suggest a new general algorith...
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in this paper, we introduce and study a new system of (A, eta)-accretive mapping inclusions in Banach spaces. Using the resolvent operator associated with (A, eta)-accretive mappings, we suggest a new general algorithm and establish the existence and uniqueness of solutions for this system of (A, eta)-accretive mapping inclusions. Under certain conditions, we discuss the convergence and stability of iterative sequence generated by the algorithm. Our results extend, improve and unify many known results on variational inequalities and variational inclusions. (C) 2008 Published by Elsevier Ltd
This paper presents a new iterative algorithm for a quasivariational inequality system related to HJB equation. A domain decomposition method based on this algorithm is proposed. The convergence theorems have been est...
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This paper presents a new iterative algorithm for a quasivariational inequality system related to HJB equation. A domain decomposition method based on this algorithm is proposed. The convergence theorems have been established. (C) 2007 Elsevier B.V. All rights reserved.
Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AXB = E that is appropriate when there is error in the matrix E. In this paper, by means of real rep...
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Quaternionic least squares (QLS) problem is one method of solving overdetermined sets of quaternion linear equations AXB = E that is appropriate when there is error in the matrix E. In this paper, by means of real representation of a quaternion matrix, we introduce a concept of norm of quaternion matrices, which is different from that in [T. Jiang, L. Chen, Algebraic algorithms for least squares problem in quaternionic quantum theory, Comput. Phys. Comm. 176 (2007) 481-485: T. Jiang, M. Wei, Equality constrained least squares problem over quaternion field, Appl. Math. Lett. 16 (2003) 883-888), and derive an iterative method for finding the minimum-norm solution of the QLS problem in quaternionic quantum theory. (C) 2008 Elsevier B.V. All rights reserved.
In this paper, we propose a Maximization-Maximization (MM) algorithm for the assessment of hidden parameters in structural credit risk models. Step M1 updates the value, volatility, and expected return on the firm'...
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In this paper, we propose a Maximization-Maximization (MM) algorithm for the assessment of hidden parameters in structural credit risk models. Step M1 updates the value, volatility, and expected return on the firm's assets by maximizing the log-likelihood function for the time series of equity prices;Step M2 updates the default barrier by maximizing the equity holders' participation in the firm's asset value. The main contribution of the method lies in the M2 step, which allows for 'endogenizing' the default barrier in light of actual data on equity prices. Using a large international sample of companies, we demonstrate that theoretical credit spreads based on the MM algorithm offer the lowest CDS pricing errors when compared to other, traditional default barrier specifications: smooth-pasting condition value, maximum likelihood estimate, KMV's default point, and nominal debt. (C) 2012 Elsevier B.V. All rights reserved.
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