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In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a finite family of mixed equilibrium problems, a general system of generalized equilibria and a fixed point problem of nonexpansive mappings in a real Hilbert space. Under some appropriate conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a weak convergence algorithm, called the linesearch algorithm, for solving a split equilibrium problem and nonexpansive mapping (SEPNM) in real Hilbert spaces, in which the first bifunction is pseudomonotone with respect to its solution set, the second bifunction is monotone, and fixed point mappings are nonexpansive. In this algorithm, we combine the extragradient method incorporated with the Armijo linesearch rule for solving equilibrium problems and the Mann method for finding a fixed point of an nonexpansive mapping. We then combine the proposed algorithm with hybrid cutting technique to get a strong convergence algorithm for SEPNM. Special cases of these algorithms are also given. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to study the proximal split feasibility problems. For solving the problems, we present new self-adaptive algorithms with the regularization technique. By using these algorithms, we give some strong convergence theorems for the proximal split feasibility problems. [ABSTRACT FROM AUTHOR]

Mean curvature-based energy minimization denoising model by Zhu and Chan offers one approach for restoring both smooth (no edges) and non-smooth (with edges) images. The resulting fourth-order partial differential equations arising from minimization of this model is non-trivial to solve due to appearance of a high nonlinearity and stiffness term, because simple alternative methods such as the fixed point method and the primal dual method do not work. In this paper, we first present a relaxed fixed point method for solving such equations and further to combine with a homotopy algorithm to achieve fast convergence. Numerical experiments show that our method is able to maintain all important information in the image, and at the same time to filter out noise. [ABSTRACT FROM PUBLISHER]

The Rudin, Osher, and Fatemi model [20] (ROF) for image restoration has been extensively studied due to its edge preserving capability, but for images without edges (jumps), the solution to this model has the undesirable staircasing effect. To improve the model, Lysaker, Lundervold and Tai [14] (LLT) proposed a better second-order functional suitable for restoring smooth images but it is difficult to preserve discontinuities for non-smooth images. It turns out that results from convex combinations of ROF model and LLT model can preserve the main advantages of both models (see [16, 9]). In this paper, we first propose an applicable homotopy algorithm based fixed point method for the LLT model. We then propose two new variants of convex combination models. Numerical experiments are shown to demonstrate the advantages of these combination models and the robustness of our homotopy algorithm. [ABSTRACT FROM AUTHOR]

Our goal in this paper is to improve the computational performance of the proximity algorithms for the L1/TV denoising model. This leads us to a new characterization of all solutions to the L1/TV model via fixed-point equations expressed in terms of the proximity operators. Based upon this observation we develop an algorithm for solving the model and establish its convergence. Furthermore, we demonstrate that the proposed algorithm can be accelerated through the use of the componentwise Gauss-Seidel iteration so that the CPU time consumed is significantly reduced. Numerical experiments using the proposed algorithm for impulsive noise removal are included, with a comparison to three recently developed algorithms. The numerical results show that while the proposed algorithm enjoys a high quality of the restored images, as the other three known algorithms do, it performs significantly better in terms of computational efficiency measured in the CPU time consumed. [ABSTRACT FROM AUTHOR]

Abstract: The truncation error of fixed-point multiplication is commonly modelled as white noise with a uniform distribution. This paper shows the inaccuracy of this assumption by using a bitwise approach. A probabilistic bit-pattern analysis of the fixed-point multiplication is presented from which an accurate probability model for the truncation error is derived. Using this PDF model, exact values for the mean and variance of the truncation error in the output of the fixed-point multiplication are formulated for the first time. The proposed PDF model, mean and variance values are compact and usable in word-length optimization algorithms. [Copyright &y& Elsevier]

In this paper, we introduce a novel way of performing real-valued optimization in the complex domain. This framework enables a direct complex optimization technique when the cost function satisfies the Brandwood's independent analyticity condition. In particular, this technique has been used to derive three algorithms, namely, kurtosis maximization using gradient update (KM-G), kurtosis maximization using fixed-point update (KM-F), and kurtosis maximization using Newton update (KM-N), to perform the complex independent component analysis (ICA) based on the maximization of the complex kurtosis cost function. The derivation and related analysis of the three algorithms are performed in the complex domain without using any complex-real mapping for differentiation and optimization. A general complex Newton rule is also derived for developing the KM-N algorithm. The real conjugate gradient algorithm is extended to the complex domain similar to the derivation of complex Newton rule. The simulation results indicate that the fixed-point version (KM-F) and gradient version (KM-G) are superior to other similar algorithms when the sources include both circular and noncircular distributions and the dimension is relatively high. [ABSTRACT FROM AUTHOR]

A measure of entanglement with respect to a bipartite partition of n-qubit has been defined and studied from the viewpoint of Riemannian geometry (Iwai 2007 J. Phys. A: Math. Theor. 40 12161). This paper has two aims. One is to study further the geometry of entanglement, and the other is to investigate Grover's search algorithms, both the original and the fixed-point ones, in reference with entanglement. As the distance between the maximally entangled states and the separable states is known already in the previous paper, this paper determines the set of maximally entangled states nearest to a typical separable state which is used as an initial state in Grover's search algorithms, and to find geodesic segments which realize the above-mentioned distance. As for Grover's algorithms, it is already known that while the initial and the target states are separable, the algorithms generate sequences of entangled states. This fact is confirmed also in the entanglement measure proposed in the previous paper, and then a split Grover algorithm is proposed which generates sequences of separable states only with respect to the bipartite partition. [ABSTRACT FROM AUTHOR]