Shin-ya Matsushita

A strong convergence theorem for relatively nonexpansive mappings in a Banach space

In this paper, we prove a strong convergence theorem for relatively nonexpansive mappings in a Banach space by using the hybrid method in mathematical programming. Using this result, we also discuss the problem of strong convergence concerning nonexpansive mappings in a Hilbert space and maximal monotone operators in a Banach space.

Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces

We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. We apply these results to the convex feasibility problem and a proximal-type algorithm for monotone operators in Banach spaces.

A New Elementary Operation Approach to Multidimensional Realization and LFR Uncertainty Modeling: The MIMO Case

This paper proposes a new elementary operation approach (EOA) to multidimensional (-D) realization and linear fractional representation (LFR) modeling for multi-input and multi-output (MIMO) -D systems, as an extension of the new EOA proposed for the single-input and single-output (SISO) case by the authors recently. It is shown that, due to the substantial differences between the SISO and MIMO systems, the extension is not straightforward and further significant development is necessary. A matrix relation property among the associated matrices under the augmenting and admissible elementary operations is first revealed. Based on this matrix relation property, the realization problem for the MIMO -D case is formulated as an elementary operation problem of a certain -D polynomial matrix, which makes the extension possible. General constructive procedures are then established for the regular realizations based on the right and left matrix fraction descriptions (MFDs) of a given transfer matrix, respectively, such that one can easily implement this approach by a computer program in, e.g., MATLAB or Maple. Numerical and symbolic examples are provided to illustrate the main ideas and the effectiveness of the proposed approach.

Approximating fixed points of nonexpansive mappings in a Banach space by metric projections

Abstract In this paper, a strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem is different from the recent strong convergence theorem due to Xu [H.K. Xu, Strong convergence of approximating fixed point sequences for nonexpansive mappings, Bull. Aust. Math. Soc. 74 (2006) 143–151] which was established by generalized projections.

Improved adaptive sparse channel estimation using mixed square/fourth error criterion

Sparse channel estimation problem is one of challenge technical issues in stable broadband wireless communications. Based on square error criterion (SEC), adaptive sparse channel estimation (ASCE) methods, e.g., zero-attracting least mean square error (ZA-LMS) algorithm and reweighted ZA-LMS (RZA-LMS) algorithm, have been proposed to mitigate noise interferences as well as to exploit the inherent channel sparsity. However, the conventional SEC-ASCE methods are vulnerable to 1) random scaling of input training signal; and 2) imbalance between convergence speed and steady state mean square error (MSE) performance due to fixed step-size of gradient descend method. In this paper, a mixed square/fourth error criterion (SFEC) based improved ASCE methods are proposed to avoid aforementioned shortcomings. Specifically, the improved SFEC-ASCE methods are realized with zero-attracting least mean square/fourth error (ZA-LMS/F) algorithm and reweighted ZA-LMS/F (RZA-LMS/F) algorithm, respectively. Firstly, regularization parameters of the SFEC-ASCE methods are selected by means of Monte-Carlo simulations. Secondly, lower bounds of the SFEC-ASCE methods are derived and analyzed. Finally, simulation results are given to show that the proposed SFEC-ASCE methods achieve better estimation performance than the conventional SEC-ASCE methods. 1

Realization of multidimensional systems in Fornasini-Marchesini state-space model

This paper presents a constructive procedure that can generate a Fornasini-Marchesini (local) state-space model realization for a given n-D system with lower order than the existing procedure given by Alpay and Dubi. It is clarified that the method of Alpay and Dubi usually generates a realization with unnecessarily high order even for a simple rational transfer function, and, by taking into account of the structural characteristic of the given transfer function or transfer matrix, it is possible to construct a realization with much lower order. Nontrivial examples are given to illustrate the basic idea as well as the effectiveness of the proposed approach.

On convergence of the proximal point algorithm in Banach spaces

In this paper, we give a sufficient condition which guarantees that the sequence generated by the proximal point algorithm terminates after a finite number of iterations.

Roesser model realization of MIMO n-D systems by elementary operations

This paper considers the Roesser state-space model realization problem for a multidimensional (n-D) system by using elementary operations. The new elementary operation approach proposed recently by the authors for the the single-input and single-output (SISO) case will be generalized to the multi-input and multi-output (MIMO) case. Specifically, the realization problem is first formulated as an elementary operation problem of some n-D polynomial matrix. Then, a general constructive realization procedure is established based on a right matrix fraction description of the given transfer matrix, which guarantees a regular realization and can be easily implemented by a computer program. An example is given to illustrate the details and effectiveness of the proposed approach.

On the convergence rate of the Krasnosel’skiĭ–Mann iteration

The Krasnosel’skiĭ–Mann (KM) iteration is a widely used method to solve fixed point problems. This paper investigates the convergence rate for the KM iteration. We first establish a new convergence rate for the KM iteration which improves the known big-

Robust stochastic gradient-based adaptive filtering algorithms to realize compressive sensing against impulsive interferences

O