COMPLETE EIGEN-SOLUTIONS FOR ANTI-PLANE NOTCHES WITH MULTI-MATERIALS BY SUPER-INVERSE ITERATION

In this paper,the super-inverse iterative method is proposed to compute the accurateand complete eigen-solutions for anti-plane cracks/notches with multi-materials,arbitrary opening an-gles and various surface conditions.Taking the advantage of the knowledge of the variation forms ofthe eigen-functions,a series of numerical techniques are proposed to simplify the computation andspeed up the convergence rate of the inverse iteration.A number of numerical examples are given todemonstrate the excellent accuracy,efficiency and reliability of the proposed approach.

A MODIFIED INVERSE ITERATION FOR A LARGE SPARSE SPD GENERALIZED EIGENPROBLEM

In this paper, an algorithm based on a shifted inverse power iteration for computing generalized eigenvalues with corresponding eigenvectors of a large scale sparse symmetric positive definite matrix pencil is presented. It converges globally with a cubic asymptotic convergence rate, preserves sparsity of the original matrices and is fully parallelizable. The algebraic multilevel itera-tion method (AMLI) is used to improve the efficiency when symmetric positive definite linear equa-tions need to be solved.

Explicit Iterative Methods of Second Order and Approximate Inverse Preconditioners for Solving Complex Computational Problems

Explicit Exact and Approximate Inverse Preconditioners for solving complex linear systems are introduced. A class of general iterative methods of second order is presented and the selection of iterative parameters is discussed. The second order iterative methods behave quite similar to first order methods and the development of efficient preconditioners for solving the original linear system is a decisive factor for making the second order iterative methods superior to the first order iterative methods. Adaptive preconditioned Conjugate Gradient methods using explicit approximate preconditioners for solving efficiently large sparse systems of algebraic equations are also presented. The generalized Approximate Inverse Matrix techniques can be efficiently used in conjunction with explicit iterative schemes leading to effective composite semi-direct solution methods for solving large linear systems of algebraic equations.

A Newton type iterative method for heat-conduction inverse problems

An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.

Sensitivity and inverse analysis methods for parameter intervals

This paper proposes a sensitivity analysis method for engineering parameters using interval analyses.This method substantially extends the application of interval analysis method.In this scheme,parameter intervals and decision-making target intervals are determined using the interval analysis method.As an example,an inverse analysis method for uncertainty is presented.The intervals of unknown parameters can be obtained by sampling measured data.Even for limited measured data,robust results can also be obtained with the inverse analysis method,which can be intuitively evaluated by the uncertainty expressed in terms of an interval.For complex nonlinear problems,an iteratively optimized inverse analysis model is proposed.In a given set of loose parameter intervals,all the unknown parameter intervals that satisfy the measured information can be obtained by an iteratively optimized inverse analysis model.The influences of measured precisions and the number of parameters on the results of the inverse analysis are evaluated.Finally,the uniqueness of the interval inverse analysis method is discussed.

Newton-type methods and their modifications for inverse heat conduction problems

This paper studies to numerical solutions of an inverse heat conduction problem.The effect of algorithms based on the Newton-Tikhonov method and the Newton-implicit iterative method is investigated,and then several modifications are presented.Numerical examples show the modified algorithms always work and can greatly reduce the computational costs.

Numerical solution of the imprecisely defined inverse heat conduction problem

This paper investigates the numerical solution of the uncertain inverse heat conduction problem. Uncertainties present in the system parameters are modelled through triangular convex normalized fuzzy sets. In the solution process, double parametric forms of fuzzy numbers are used with the variational iteration method(VIM). This problem first computes the uncertain temperature distribution in the domain. Next, when the uncertain temperature measurements in the domain are known, the functions describing the uncertain temperature and heat flux on the boundary are reconstructed. Related example problems are solved using the present procedure. We have also compared the present results with those in [Inf.Sci.(2008) 178 1917] along with homotopy perturbation method(HPM) and [Int. Commun. Heat Mass Transfer(2012) 3930] in the special cases to demonstrate the validity and applicability.

Inverse Analysis of Origin-Destination Matrix for Microscopic Traffic Simulator

Microscopic traffic simulations are useful for solving various trafficrelated problems,e.g.traffic jams and accidents,local and global environmental and energy problems,maintaining mobility in aging societies,and evacuation planning for natural as well as man-made disasters.The origin-destination(OD)matrix is often used as the input to represent traffic demands into traffic simulators.In this study,we propose an indirect method for estimating the OD matrix using a traffic simulator as an internal model.The proposed method is designed to output results that are consistent with the input of the simulator.The method consists of the following steps:(1)calculating link traffic volume from the OD matrix,and(2)updating the matrix.The estimated matrix is updated iteratively until it converges to a predefined tolerance level.Numerical experiments are then conducted using the proposed method on a grid network and on a representation of an actual road network.Finally,we discuss the characteristics of the proposed method and the non-negative constraint for the traffic volume.

On Computer Implementation for Comparison of Inverse Numerical Schemes for Non-Linear Equations

In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3.Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3.Using computer algebra system Mathematica,we find the lower bound of the convergence order and verify it theoretically.Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods.Some non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods.Computational CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.

A Class of Generalized Approximate Inverse Solvers for Unsymmetric Linear Systems of Irregular Structure Based on Adaptive Algorithmic Modelling for Solving Complex Computational Problems in Three Space Dimensions

A class of general inverse matrix techniques based on adaptive algorithmic modelling methodologies is derived yielding iterative methods for solving unsymmetric linear systems of irregular structure arising in complex computational problems in three space dimensions. The proposed class of approximate inverse is chosen as the basis to yield systems on which classic and preconditioned iterative methods are explicitly applied. Optimized versions of the proposed approximate inverse are presented using special storage (k-sweep) techniques leading to economical forms of the approximate inverses. Application of the adaptive algorithmic methodologies on a characteristic nonlinear boundary value problem is discussed and numerical results are given.

INCOMPLETE SEMI-ITERATIVE METHODS FOR SOLVING SINGULAR LINEAR OPERATOR EQUATIONS IN BANACH SPACE WITH APPLICATIONS IN MARKOV CHAIN MODELING

We discuss the incomplete semi-iterative method (ISIM) for an approximate solution of a linear fixed point equations x=Tx+c with a bounded linear operator T acting on a complex Banach space X such that its resolvent has a pole of order k at the point 1. Sufficient conditions for the convergence of ISIM to a solution of x=Tx+c, where c belongs to the range space of R(I-T) k, are established. We show that the ISIM has an attractive feature that it is usually convergent even when the spectral radius of the operator T is greater than 1 and Ind 1T≥1. Applications in finite Markov chain is considered and illustrative examples are reported, showing the convergence rate of the ISIM is very high.

A distributed inverse iteration method for eigenvalue analysis of interconnected power systems

Since China power grids have a hierarchical architecture in operation and man- agement, centralized computation patterns are difficult to meet the demands of small-signal-stability analysis of the bulk interconnected power systems. A dis- tributed eigenvalue algorithm derived from the inverse iteration method is pro- posed. It can not only obtain eigenvalues and eigenvectors from power system state matrix but also provide participation factors of all generators. In the comput- ing process, the algorithm only requires exchanging data of boundary nodes and a small amount of other information of different regions. Therefore, it is very suitable to be deployed in a WAN (wide area network) based distributed environment. The algorithm has been tested on an IEEE39 system.

基于Iterative映射和单纯形法的改进灰狼优化算法

为了解决基本灰狼优化算法(GWO)依赖初始种群和求解精度不高的问题,提出一种基于Iterative映射和单纯形法的改进灰狼优化算法(SMIGWO)。该算法利用混沌Iterative映射产生初始灰狼种群,增强全局搜索过程中的种群多样性;采用逆不完全Γ函数更新收敛因子,以平衡算法的全局搜索和局部搜索能力;利用单纯形法的反射、扩张和收缩操作对当前较差个体进行改进,避免算法陷入局部最优。对10个测试函数进行仿真实验,数值结果表明,与基本GWO算法、Square GWO算法、非线性收敛因子的GWO(NGWO)算法、混合GWO(HGWO)算法、粒子群优化算法(PSO)、细菌觅食算法(BFA)和引力搜索算法(GSA)相比,改进的灰狼优化算法求解精度更高,稳定性更好。

Acoustic impedance inversion of zero-offset VSP data

高度精确的声学的阻抗倒置是为预先钻的一种关键技术由 VSP 数据的预言。在这篇论文，基于 VSP 数据有高分辨率的事实，高发信号到噪音比率，并且下面去并且在去上面，波浪能精确地被分开，我们建议用 VSP 数据在位前面在地上凿穿下面预言阻抗的一个方法。首先，非线性的反复的倒置的方法被采用用 VSP 走廊栈为阻抗转换。然后，由在重复并且用 preconditioned 修改抑制因素结合坡度方法解决倒置结果的方程，稳定性和集中能被提高。理论模型和实际数据的结果证明方法为预先钻是有效的预言使用 VSP 数据。

Autofocus technique for ISAR imaging of uniformly rotating targets based on the ExCoV method

The inverse synthetic aperture radar(ISAR) imaging can be converted into a sparse reconstruction problem and solved by the l_1-norm minimization algorithm. The basis matrix in sparse ISAR imaging is usually characterized by the unknown rotation rate of a moving target, thus the rotation rate and the sparse signal should be jointly estimated. Especially due to the imperfect coarse motion compensation, we consider the phase error correction problem in the context of the sparse signal reconstruction. To address this issue, we propose an iterative reweighted method,which jointly estimates the rotation rate, corrects the phase error and reconstructs a high resolution ISAR image. The proposed method gives a gradual and interweaved iterative process to refine the unknown parameters to achieve the best sparse representation for the ISAR signals. Particularly, in ISAR image reconstruction,the l_1-norm minimization algorithm is sensitive to user parameters.Setting these user parameters are not trivial and the reconstruction performance depends significantly on their choices. Then, we consider an expansion-compression variance-component(ExCoV) based method, which is automatic and demands no prior knowledge about signal-sparsity or measurement-noise levels. Both numerical and electromagnetic data experiments are implemented to show the effectiveness of the proposed method. It is shown that the proposed method can estimate the rotation rate and correct the phase errors simultaneously, and its superior performance is proved in terms of high resolution ISAR image.

Computational Methods in the Theory of Synthesis of Radio and Acoustic Radiating Systems

A brief review of the works of the author and his co-authors on the application of nonlinear analysis, numerical and analytical methods for solving the nonlinear inverse problems (synthesis problems) for optimizing the different types of radiating systems, is presented in the paper. The synthesis problems are formulated in variational statements and further they are reduced to research and numerical solution of nonlinear integral equations of Hammerstein type. The existence theorems are proof, the investigation methods of nonuniqueness problem of solutions and numerical algorithms of finding the optimal solutions are proved.

Magnetotelluric data inversion with seismic data constraint

In the paper we present a new method to invert the interior structure in the basement or ancient hidden hill by us-ing magnetotelluric (MT) data with seismic data constraint. We first obtain the thickness and resistivity of each layer above the basement or buried hill by the inversion of seismic and log data and create a geoelectrical model for the layers above the basement or hidden hill. Then with the reference to the inversion of 1D MT data, a geoelectrical model for the layers below the basement or hidden hill is created. On the basis of the above initial model, we present an effective and practical forward method, i.e., a model-matched approach to conduct forward inversion arithmetic. Finally, by the method of conjugate gradient iteration, a forward and backward iterative cal-culation is made. Taking No. 618 profile of Shengli Oil Field as an example, we have found out that the tectonic information that is unreflective in the seismic data below the basement is better reflected in the inversion result.

AN ADAPTIVE INVERSE ITERATION FEM FOR THE INHOMOGENEOUS DIELECTRIC WAVEGUIDES

我们为计算电磁的指导波浪在介绍一个适应有限元素方法一关门，不同类， pillared 在给定的频率的三维的 wavegnide 基于反的重复方法。这个问题作为一个概括特征值被提出问题。由为特征值问题修改准确反的重复算法，我们设计一次新适应反的重复有限元素算法。适应有限元素方法基于后验错误估计知道在解决败坏的特徵函数的奇特成功的斧子有限元素集中。我们为电磁的指导波浪问题构造后验错误评估者。报导说明我们的适应反的重复的伪最佳的表演的数字结果斧子有限元素方法。数学题目分类：65N30， 65N25， 78A50。

无RSM参数的反解RFM求解方法

为实现在无严格传感器模型(RSM)参数的条件下求解反解RFM,提出一种基于正解RFM的反解RFM求解方法。首先通过正解RFM生成虚拟控制格网,建立反解RFM求解流程;然后考虑误差法矩阵病态对求解结果的影响,采用岭参数谱修正迭代与LDLT分解,提升求解的效率和精度;最后以影像立体定位为例,验证了所求解的反解RFM在影像处理中的有效性。实验结果表明:所提方法是对RSM的另一种高精度拟合,在影像立体定位应用中,同正解RFM精度基本相当,且具有更高的立体定位效率,为反解RFM的后续应用提供了良好基础。

求解逆矩阵的牛顿迭代法

在线性代数课程中,关于逆矩阵的求解有很多方法,但均不适合在计算机上实现。文章将牛顿迭代法应用到逆矩阵的求解过程中,给出了求解逆矩阵的牛顿迭代法。实验结果表明,该算法是一种有效的算法,并且特别适合在计算机上进行计算。