In this paper, we give the notion of P-eta-proximal mapping, an extension of P-proximal mapping given by Ding and Xia [J. Comput. Appl. Math. 147 (2002) 369], for a nonconvex lower semicontinuous eta-subdifferentiable...
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In this paper, we give the notion of P-eta-proximal mapping, an extension of P-proximal mapping given by Ding and Xia [J. Comput. Appl. Math. 147 (2002) 369], for a nonconvex lower semicontinuous eta-subdifferentiable proper functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a class of generalized set-valued variational-like inclusions in Banach space and show its equivalence with a class of implicit Wiener-Hopf equations using the concept of P-eta-proximal mapping. Using this equivalence, we propose a new class of iterative algorithms for the class of generalized set-valued variational-like inclusions. Furthermore, we prove the existence of solution of generalized set-valued variational-like inclusions and discuss the convergence criteria and the stability of the iterative algorithm. (c) 2004 Elsevier Inc. All rights reserved.
In this paper, we propose a new iterative algorithm and analyze it in detail inasmuch as convergence, stability, and data dependency for the class of almost contraction mappings. We also consider another iterative alg...
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In this paper, we propose a new iterative algorithm and analyze it in detail inasmuch as convergence, stability, and data dependency for the class of almost contraction mappings. We also consider another iterative algorithm called F* iterative algorithm proposed by Ali et al. (Comp. Appl. Math. 39, 267 (2020)) and derive some new algorithms from this with the aim of giving an affirmative answer to an open question raised by the same authors. Our results considerably improve the corresponding results in Ali et al. (Comp. Appl. Math. 39, 267 (2020)). We submit some non-trivial numerical examples to illustrate the robustness, feasibility, and effectiveness of our findings.
Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. Based on Paige's algorithms LSQR and residual-reducing version of LSQR proposed in Paige and...
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Quaternionic least squares (QLS) is an efficient method for solving approximate problems in quaternionic quantum theory. Based on Paige's algorithms LSQR and residual-reducing version of LSQR proposed in Paige and Saunders [LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Softw. 8(1) (1982), pp. 4371], we provide two matrix iterative algorithms for finding solution with the least norm to the QLS problem by making use of structure of real representation matrices. Numerical experiments are presented to illustrate the efficiency of our algorithms.
A new method for the acceleration of explicit iterative algorithms for the numerical solution of systems of partial differential equations has been developed. The method is based on the idea of allowing each partial d...
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A new method for the acceleration of explicit iterative algorithms for the numerical solution of systems of partial differential equations has been developed. The method is based on the idea of allowing each partial differential equation in the system to approach the converged solution at its own optimal speed and at the same time to communicate with the rest of the equations in the system.
This paper addresses the problem of digital blind restoration of images degraded by space-variant blurs and noise. The existing Expectation-Maximization (EM) algorithm reported in the literature is extended in this pa...
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This paper addresses the problem of digital blind restoration of images degraded by space-variant blurs and noise. The existing Expectation-Maximization (EM) algorithm reported in the literature is extended in this paper and combined with the region adaptive technique to handle the problem of identifying spatially variant blurs. The proposed algorithm is a two-step interative process. The expectation step of the EM algorithm is modified by the use of iterative image restoration. The entire image is divided into disjointed regions and the blur is identified in these regions using the proposed modified form of the EM algorithm. The iterative Constrained Least Squares (CLS) algorithm used in space-invariant image restoration is extended to restore the space variant blur images. Spatially adaptive algorithms for restoration are also applied. Experiments have been carried out to evaluate the performances of the proposed algorithms.
The parallelization of iterative algorithms is an important issue for efficient solution of large numerical problems. Several theoretical results concerning sufficient conditions for. and speed of convergence of paral...
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The parallelization of iterative algorithms is an important issue for efficient solution of large numerical problems. Several theoretical results concerning sufficient conditions for. and speed of convergence of parallel iterative algorithms are available. However, those results usually do not take into account the processor workloads and network communications at the application level. The approach in this paper develops a Markov chain based on random variables which describe aspects of the multiuser, distributed-memory environment and the phases of the algorithm. The performance characterization addresses stochastic characteristics of the algorithmic execution time such as mean values and standard deviations. We present simulation results as well as experimental results over different time periods. The results provide information about the impact of distributed environment and implementation style on long-run expected execution time characteristics. (C) Academic Press.
Based on the analysis of the feature of cognitive radio networks, a relevant interference model was built. Cognitive users should consider especially the problem of interference with licensed users and satisfy the sig...
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Based on the analysis of the feature of cognitive radio networks, a relevant interference model was built. Cognitive users should consider especially the problem of interference with licensed users and satisfy the signal-to-interference noise ratio （SINR） requirement at the same time. According to different power thresholds, an approach was given to solve the problem of coexistence between licensed user and cognitive user in cognitive system. Then, an uplink distributed power control algorithm based on traditional iterative model was proposed. Convergence analysis of the algorithm in case of feasible systems was provided. Simulations show that this method can provide substantial power savings as compared with the power balancing algorithm while reducing the achieved SINR only slightly, since 6% S1NR loss can bring 23% power gain. Through further simulations, it can be concluded that the proposed solution has better effect as the noise power or system load increases.
Let C be a nonempty closed convex subset of a real Hilbert space, and let T : C -> C be an asymptotically k-strictly pseudocontractive mapping with F(T) = {x is an element of C : Tx = x} not equal = empty set. Let ...
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Let C be a nonempty closed convex subset of a real Hilbert space, and let T : C -> C be an asymptotically k-strictly pseudocontractive mapping with F(T) = {x is an element of C : Tx = x} not equal = empty set. Let {alpha(n)}(n=1)(infinity) and {t(n)}(n=1)(infinity) be real sequences in (0, 1). Let {x(n)}(n=1)(infinity) be the sequence generated from an arbitrary x(1) is an element of C by {v(n) = P-C((1 - t(n))x(n)), n >= 1, x(n+1) = (1 - alpha(n))v(n) + alpha(n)T(n)v(n), n >= 1, where P-C : H -> C is the metric projection. Under some appropriate mild conditions on {alpha(n)}(n=1)(infinity) and {t(n)}(n=1)(infinity), we prove that {x(n)}(n=1)(infinity) converges strongly to a fixed point of T. Furthermore, if T : C -> C is uniformly L-Lipschitzian and asymptotically pseudocontractive with F(T) not equal empty set, we first prove that (I - T) is demiclosed at 0, and then prove that under some suitable conditions on the real sequences {a(n)}(n=1)(infinity), {beta(n)}(n=1)(infinity) and {t(n)}(n=1)(infinity) in (0, 1), the sequence {x(n)}(n=1)(infinity) generated from an arbitrary x(1) -> C by {v(n) = PC((1 - t(n))x(n)), n >= 1, y(n) = (1 - beta(n))v(n) + beta(n)T(n)v(n), n >= 1, x(n+1) = (1 - alpha(n))v(n) + alpha(n)T(n)y(n), n >= 1, converges strongly to a fixed point of T. No compactness assumption is imposed on T or C and no further requirement is imposed on F(T).
This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB + (CXD)-D-T = F. The basic idea is to decompose the matrix equation (system) under consideration into...
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This paper develops a gradient based and a least squares based iterative algorithms for solving matrix equation AXB + (CXD)-D-T = F. The basic idea is to decompose the matrix equation (system) under consideration into two subsystems by applying the hierarchical identification principle and to derive the iterative algorithms by extending the iterative methods for solving Ax = b and AXB = F. The analysis shows that when the matrix equation has a unique solution (under the sense of least squares), the iterative solution converges to the exact solution for any initial values. A numerical example verifies the proposed theorems. (C) 2010 Elsevier Inc. All rights reserved.
In this paper, we extend the auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities. We prove the existence of a solution of the auxiliary probl...
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In this paper, we extend the auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities. We prove the existence of a solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities, construct the iterative algorithm for the generalized set-valued strongly nonlinear mixed variational-like inequalities, and show the existence of a solution of the generalized set-valued strongly nonlinear mixed variational-like inequality by using the auxiliary principle technique. We also prove the convergence of iterative sequences generated by the algorithm. (C) 2001 Academic Press.
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