Nonlinear implicit iterative method for solving nonlinear ill-posed problems

In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.

Mechanical quadrature methods and extrapolation for solving nonlinear boundary Helmholtz integral equations

This paper presents mechanical quadrature methods （MQMs） for solving nonlinear boundary Helmholtz integral equations. The methods have high accuracy of order O（h3） and low computation complexity. Moreover, the mechanical quadrature methods are simple without computing any singular integration. A nonlinear system is constructed by discretizing the nonlinear boundary integral equations. The stability and convergence of the system are proved based on an asymptotical compact theory and the Stepleman theorem. Using the h3-Richardson extrapolation algorithms （EAs）, the accuracy to the order of O（h5） is improved. To slove the nonlinear system, the Newton iteration is discussed extensively by using the Ostrowski fixed point theorem. The efficiency of the algorithms is illustrated by numerical examples.

ON ITERATIVE ALGORITHMS FOR A CLASS OF NONLINEAR VARIATIONAL INEQUALITIES

In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.

MODELS OF ASYNCHRONOUS MRALLEL NONLINEAR MULTISPLITTING RELAXED ITERATIONS

In the sense of the nonlinear multisplitting and based on the principle of suffi-ciently using the delayed information, we propose models of asynchronous parallelaccelerated overrelaxation iteration methods for solving large scale system of non-linear equations. Under proper conditions, we set up the local convergence theoriesof these new method models.

Internal Force Analysis Due to the Supporting Translation in Statically (Indeterminate) Structures for Different Elastic Modulus

For statically indeterminate structure, the internal force will be changed with the translation of the supports, because the internal force is related to the absolute value of the stiffness EI. When the tension is different with the compression modulus, EI is the function of internal force and is not constant any more that is different from classic mechanics. In the other words, it is a nonlinear problem to calculate the internal force. The expression for neutral axis of the statically indeterminate structure was derived in the paper. The iterative program for nonlinear internal force was compiled. One case study was presented to illustrate the difference between the results using the different modulus theory and the single modulus theory as in classical mechanics. Finally, some reasonable suggestions were made for the different modulus structures.

INVERSION OF MOISTURE PROFILES BY A NONLINEAR ITERATIVE PHYSICAL RETRIEVAL

The Advanced TIROS-N Operational Vertical Sounder (ATOVS) measurements are used to generate the atmospheric parameters,such as temperature and moisture profiles,under both clear and cloudy situations.This paper describes briefly the nonlinear iterative physical retrieval method.By using this retrieval scheme,an experiment has been carried out to retrieve the moisture profiles from ATOVS measurements on the NOAA-16 satellite for July of 2002.ATOVS profile retrieval results are evaluated by root mean square (RMS) differences with respect to RAdiosonde OBservation (RAOB) profiles.The accuracy of the retrieval is about 15%-23% for the relative humidity profile in this study.

NONLINEAR RANK-ONE MODIFICATION OF THE SYMMETRIC EIGENVALUE PROBLEM

Nonlinear rank-one modification of the symmetric eigenvalue problem arises from eigenvibrations of mechanical structures with elastically attached loads and calculation of the propagation modes in optical fiber. In this paper, we first study the existence and uniqueness of eigenvalues, and then investigate three numerical algorithms, namely Picard iteration, nonlinear Rayleigh quotient iteration and successive linear approximation method （SLAM）. The global convergence of the SLAM is proven under some mild assumptions. Numerical examples illustrate that the SLAM is the most robust method.

Picard-Newton Iterative Method with Time Step Control for Multimaterial Non-Equilibrium Radiation Diffusion Problem

For a new nonlinear iterative method named as Picard-Newton(P-N)iterative method for the solution of the time-dependent reaction-diffusion systems,which arise in non-equilibrium radiation diffusion applications,two time step control methods are investigated and a study of temporal accuracy of a first order time integration is presented.The non-equilibrium radiation diffusion problems with flux limiter are considered,which appends pesky complexity and nonlinearity to the diffusion coef-ficient.Numerical results are presented to demonstrate that compared with Picard method,for a desired accuracy,significant increase in solution efficiency can be obtained by Picard-Newton method with the suitable time step size selection.