Construction and Analysis of Structured Preconditioners for Block Two-by-Two Matrices

For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.

Block Iterative STMV Algorithm and Its Application in Multi-Targets Detection

STMV beamforming algorithm needs inversion operation of matrix, and its engineering application is limited due to its huge computational cost. This paper proposed block iterative STMV algorithm based on one-phase regressive filter, matrix inversion lemma and inversion of block matrix. The computational cost is reduced approximately as 1/4 M times as original algorithm when array number is M. The simulation results show that this algorithm maintains high azimuth resolution and good performance of detecting multi-targets. Within 1 - 2 dB directional index and higher azimuth discrimination of block iterative STMV algorithm are achieved than STMV algorithm for sea trial data processing. And its good robustness lays the foundation of its engineering application.

Inertial projection algorithms for convex feasibility problem

The purpose of this paper is to apply inertial technique to string averaging projection method and block-iterative projection method in order to get two accelerated projection algorithms for solving convex feasibility problem.Compared with the existing accelerated methods for solving the problem,the inertial technique employs a parameter sequence and two previous iterations to get the next iteration and hence improves the flexibility of the algorithm.Theoretical asymptotic convergence results are presented under some suitable conditions.Numerical simulations illustrate that the new methods have better convergence than the general projection methods.The presented algorithms are inspired by the inertial proximal point algorithm for finding zeros of a maximal monotone operator.

THE SIMPLE BLOCK ITERATIVE ALGORITHM OF AN EXTENDED ENTROPY MODEL AND ITS CONVERGENCE

The paper discusses an extended entropy model for the prediction of trip amount and provides a method to solve it, called the simple block iterative algorithm, from the point of view of the system of nonlinear equations. Because the algorithm gives consideration to the characteristic of the model, it has better effect in our practice. The paper also studies the existence and uniqueness of the solution and convergence of the algorithm.

Modified Block Iterative Method for Solving Convex Feasibility Problem, Equilibrium Problems and Variational Inequality Problems

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-C-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem （CFP） and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.

NonlinearAsynchronousBlockIterativeMethod

This paper proposes a class of asynchronous block iterative methods for solving large scale nonlinear equations F(x)=0 and proves local convergence. This method splits F into p blocks, then does the asynchronous parallel iteration on the p multiprocessor with shared memory. Because each processor need only solve equations with a low dimension and there is no synchronous waiting time, the parallel efficiency can be increased. Finally, we give the results of the numerical test of three kinds of Newton like asynchronous block iteration methods which run well on a multiprocessor system. These results show that the parallel efficiency is very high.

A novel TS-EIA-PTS PAPR reduction algorithm for optical OFDM systems

Because the partial transmit sequence(PTS) peak-to-average power ratio(PAPR) reduction technology for optical orthogonal frequency division multiplexing(O-OFDM) systems has higher computational complexity, a novel two-stage enhanced-iterative-algorithm PTS(TS-EIA-PTS) PAPR reduction algorithm with lower computational complexity is proposed in this paper. The simulation results show that the proposed TS-EIA-PTS PAPR reduction algorithm can reduce the computational complexity by 18.47% in the condition of the original signal sequence partitioned into 4 sub-blocks at the remaining stage of n-d=5. Furthermore, it has almost the same PAPR reduction performance and the same bit error rate(BER) performance as the EIA-PTS algorithm, and with the increase of the subcarrier number, the computational complexity can be further reduced. As a result, the proposed TS-EIA-PTS PAPR reduction algorithm is more suitable for the practical O-OFDM systems.