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In this paper, an implicit iterative algorithm is developed to obtain the unique positive definite solution of the generalized algebraic Riccati matrix equation. For this proposed algorithm, there exisits a tuning parameter which can be chosen such that this algorithm achieves better convergence performance. Some convergence results are given for the proposed algorithm. Moreover, an approach is also...
This paper studies the average consensus problem for a discrete-time multi-agent system with first-order dynamics, we provide the sufficient and necessary stable condition that the step-size needs to satisfy for the multi-agent systems with an iterative method, and the cause of oscillation is investigated with use of matrix diagonal and eigenvalue analysis method. Some conclusions about the largest...
Multiview canonical correlation analysis (MCCA) is an effective tool for analyzing the relationships among group- aligned multidimensional samples, which has been applied to the fields of pattern recognition and computer vision. In MCCA, its first-stage canonical variables are solved by a multivariate eigenvalue problem that can be computed by Horst method. However, how to use the algorithm for effectively...
The paper proposes iterative data-driven generalized minimum variance (GMV) regulatory control via L2 — regularization. The proposed approach reformulates the derivation of the GMV regulatory control as a L2-regularized optimization problem, and employs an iterative design approach that repeats the same routine as the one-shot GMV regulatory control via L2-regularization. The L2-regularization assures...
In this paper, we introduce an improved version of the recent noise reducer named zero phase method which can reduce white and impulse noises simultaneously without a priori information. The key idea of the proposed method is to apply the zero phase method iter-atively, whose theoretical justification is also provided in this paper. We also confirm the noise reduction performance of the proposed method...
In this paper, we prove the convergence and determine the best convergence factor of the gradient-based iterative algorithm for the equation Ax = b by analyzing the eigenvalues of the relevant matrices. A new property of eigenvalues related to the symmetric positive definite matrix is established. By using this property, we obtain a family of iterative algorithms for the linear matrix equation and...
This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been low-pass/band-limitedness of the underlying graph signal. However, inspired by the findings on sparse signal reconstruction, we consider the graph signal to be rather sparse/compressible in the Graph Fourier Transform (GFT) domain and propose...
In this paper, an implicit iterative algorithm is proposed to obtain the unique positive definite solution of the continuous algebraic Riccati matrix equation. In this proposed algorithm, there exists a tuning parameter which can be appropriately chosen such that the algorithm achieves better convergence performance. A sufficient condition is given for the convergence of the proposed algorithm. Moreover,...
In this paper, we consider the energy efficiency maximization problem in downlink multi-input multi-output (MIMO) multi-cell systems, where all users suffer from inter-cell interference. To solve this optimization problem with a nonconcave objective function and a complex-valued matrix variable, we extend the recently developed successive pseudo-convex approximation framework and propose a novel iterative...
The current level of computing and microprocessor technology development allows us to implement any technical objects control principles. Of considerable interest are the optimum control principles where the exclusive place is taken by the extreme processing speed problem. Despite advances in the optimum control theory and practice, there are still a lot of unresolved relevant and complex problems...
We have discuss in the paper the stability results of tangent & inverse tangent functions using Jungck Ishikawa Iterative scheme. In previous year there have been research papers in which only mathematical explanation for trigonometric functions is discuss but in this paper we have generated Mandelbrot and Julia sets and discuss their characteristics using this iterative scheme.
A problem of terminal control with linear dynamics on a finite time interval is considered. The right-hand end of trajectory is defined implicitly as a solution of boundary-value problem. The problem is reduced to finding a saddle point of the Lagrange function, and linear dynamics is regarded as an equality-type constraint. Dual extraproximal iterative method for solving the problem was proposed,...
The paper gives analytical results on convergence property for the iterative data-driven PID gain tuning based on generalized minimum variance (GMV) regulatory control. The method can achieve improved PID gains based on generalized minimum variance evaluation without using a process model. Originally, the method has been developed for non-iterative control parameter tuning method, such as Virtual...
This paper studies the path-following method for solving static output feedback (SOF) problems. In order to find initial values for the method, a new linear matrix inequality (LMI) based iterative algorithm is given by a new stabilization criterion. Then, the convergence of the improved path-following method (IPFM) is proved. Based on the above two parts, a hybrid path-following method (HPFM) is proposed...
The method of exact relaxation (ER) makes it possible to accelerate and stabilize the convergence of single-point iterative methods, but in multidimensional cases there exists “sphere of idling”, if hit by a value delivered by the basic algorithm, ER leaves the value unchanged despite computational expenses have already been done. From the other hand, a volume of the sphere is null. Therefore, deterministic...
Least squares problems on graphs are a large subclass of numerical linear algebra problems that may arise from many different applications, e.g., ranking problems, distributed clock synchronization, ranking, and arbitrage detection. Solutions to these problems are very practical and as scalability becomes a prevalent issue, researchers are working to identify algorithms most appropriate to solve these...
The technique hereinafter referred to as “differentiation by iteration” can be used in the study of the rate of convergence of iterative methods. The area of its application is essentially extended to the set of non-differentiable functions by introducing a notuon of a half-derivatives.
This paper examines the nonconvex quadratically constrained quadratic programming (QCQP) problems using a decomposition method. It is well known that a QCQP can be transformed into a rank-one constrained optimization problem. Finding a rank-one matrix is computationally complicated, especially for large scale QCQPs. A decomposition method is applied to decompose the single rank-one constraint on original...
Finding a common point of multiple closed sets in a real Hilbert space has been an important task in a wide range of signal processing. In this paper, we study asymptotic properties of the parallel projection method (PPM) for closed sets satisfying a special feasibility condition, which holds in the context of certain sparse signal processing. Our analysis guarantees that the cluster point set of...
We present an incremental Broyden-Fletcher-Goldfarb-Shanno (BFGS) method as a quasi-Newton algorithm with a cyclically iterative update scheme for solving large-scale optimization problems. The proposed incremental quasi-Newton (IQN) algorithm reduces computational cost relative to traditional quasi-Newton methods by restricting the update to a single function per iteration and relative to incremental...
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