Iteration convergence condition modeling for single spaceborne SAR image direct positioning

Single SAR image direct positioning is to determine the ground coordinate for each pixel in the SAR image assisted with a reference DEM.During this procedure,an iterative procedure is essentially needed to solve the uncertainty in elevation of each pixel in the SAR image.However,such an iterative procedure may suffer from the problem of divergence in shaded and serious layover areas.To investigate this problem,we performed a theoretical analysis on the convergence conditions that has not been intensively studied till now.The Range-Doppler(RD)model was simplified and then the general surface is degenerated into a planar surface.Mathematical deduction was then carried out to derive the convergence conditions and the impact factors for the convergence speed were evaluated.The theoretical findings were validated by experiments for both simulated and real scenarios.

ON CONVERGENCE OF ISHIKAWA ITERATION PROCEDURES WITH ERRORS

The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbitrary Banach spaces. As the direct applications, some stability results of the Ishikawa iteration methods for φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type are also given. Our results in this paper improve and extend the recent results due to Osilike and other authors.

New Estimates for the Rate of Convergence of the Method of Subspace Corrections

We discuss estimates for the rate of convergence of the method of successive subspace corrections in terms of condition number estimate for the method of parallel subspace corrections.We provide upper bounds and in a special case,a lower bound for preconditioners defined via the method of successive subspace corrections.

CONVERGENCE OF PRECONDITIONED GAUSS-SEIDEL ITERATIVE METHODS

Let the linear system Ax=b where the coefficient matrix A=(aij)∈Rm,n is an L-ma-trix(that is,aij】0 （?） i and aij≤0 （?） i≠j),A=I-L-U,I is the identity matrix,-L and-U are,respectively,strictly lower and strictly upper triangular parts of A.In[1]theauthors considered two preconditioned linear systems?x=（?） and ?x=（?）

Improved iterative convergence method in Q-ary LDPC coded high order PR-CPM

The Q-ary low-density parity-check（LDPC） coded high order partial response continuous phase modulation（PR-CPM） with double iterative loops is investigated. This scheme shows significant improvements in power and bandwidth efficiency, but at the expense of long iterative decoding delay and computational complexity induced by the improper match between the demodulator and the decoder. To address this issue, the convergence behavior of Q-ary LDPC coded CPM is investigated for the Q=2 and Q〉2 cases, and an optimized design method based on the extrinsic information transfer chart is proposed to improve the systematic iterative efficiency. Simulation results demonstrate that the proposed method can achieve a perfect tradeoff between iterative decoding delay and bit error rate performance to satisfy real-time applications.

Linear inversion-imaging method based on joint primary refl ected waves and surface-related multiples

In marine seismic exploration,especially in deep-water and hard ocean-bottom cases,free-surface multiples are strongly developed.Compared with primary waves,the wider illumination aperture of the multiples is beneficial for high-resolution seismic imaging.In this study,by introducing a new compound source composed of primaries and free-surface multiples and by ignoring internal multiples,we derive a new linearized forward problem(free-surface-multiple prediction model)under a weak-scattering assumption(i.e.,first-order Born approximation).On the basis of the new linearized problem,we propose a joint inversion-imaging method by simultaneously using the primaries and free-surface multiples under the general framework of least square inversion.To eliminate the crosstalk artifacts introduced by the cross-correlation of multiples with different orders,we prove that the crosstalk artifacts can be gradually eliminated during the inversion if a proper step length is selected.Synthetic-andfield-data tests demonstrate the effectiveness of the proposed method.

A Simple Method of Calculating the Optimal Step Size in 4DVAR Technique

In four—dimensional variational data assimilation (4DVAR) technology, how to calculate the optimal step size is always a very important and indeed difficult task. It is directly related to the computational efficiency. In this research, a new method is proposed to calculate the optimal step size more effectively. Both nonlinear one—dimensional advection equation and two—dimensional inertial wave equation are used to test and compare the influence of different methods of the optimal step size calculations on the iteration steps, as well as the simulation results of 4DVAR processes. It is in evidence that the different methods have different influences. The calculating method is very important to determining whether the iteration is convergent or not and whether the convergence rate is large or small. If the calculating method of optimal step size is properly determined as demonstrated in this paper, then it can greatly enlarge the convergence rate and further greatly decrease the iteration steps. This research is meaningful since it not only makes an important improvement on 4DVAR theory, but also has useful practical application in improving the computational efficiency and saving the computational time. Key words 4DVAR - Optimal step size - Iterative convergence rate This work was supported by the National Natural Science Foundation under grants: 49735180 and 49675259, the “973 Project? CHERES(G 1998040907), the Project of Natural Science Foundation of Jiangsu Province(BK99020), and the Project Sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars.

The convergence properties of infeasible inexact proximal alternating linearized minimization

The proximal alternating linearized minimization(PALM)method suits well for solving blockstructured optimization problems,which are ubiquitous in real applications.In the cases where subproblems do not have closed-form solutions,e.g.,due to complex constraints,infeasible subsolvers are indispensable,giving rise to an infeasible inexact PALM(PALM-I).Numerous efforts have been devoted to analyzing the feasible PALM,while little attention has been paid to the PALM-I.The usage of the PALM-I thus lacks a theoretical guarantee.The essential difficulty of analysis consists in the objective value nonmonotonicity induced by the infeasibility.We study in the present work the convergence properties of the PALM-I.In particular,we construct a surrogate sequence to surmount the nonmonotonicity issue and devise an implementable inexact criterion.Based upon these,we manage to establish the stationarity of any accumulation point,and moreover,show the iterate convergence and the asymptotic convergence rates under the assumption of the Lojasiewicz property.The prominent advantages of the PALM-I on CPU time are illustrated via numerical experiments on problems arising from quantum physics and 3-dimensional anisotropic frictional contact.

ON THE COMPLEX OSCILLATION OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS WITH MEROMORPHIC COEFFICIENTS

In this paper, we investigate the complex oscillation of higher order homogenous and non- homogeneous linear differential equations with meromorphic coefficients of iterated order, and obtain some results which improve and extend those given by Z. X. Chen, L. Kinnunen, etc.

ON THE ITERATED ORDER OF MEROMORPHIC SOLUTIONS OF HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS

In this paper, we investigate complex homogeneous and non-homogeneous higher order linear differential equations with meromorphic coefficients. We obtain several results concerning the iterated order of meromorphic solutions, and the iterated convergence exponent of the zeros of meromorphic solutions.

Evolution,Extinction,Homology and Homoplasy of the Larger Benthic Foraminifera from the Carboniferous to the Present Day,as Exemplified by Planispiral-Fusiform and Discoidal Forms

Examples of evolution,extinction and homoplasy of the larger benthic foraminifera(LBF)occur throughout their history.Since the Carboniferous,LBF have thrived in carbonate-rich tropical and subtropical shallow-marine shelf environments.Their high abundance and diversity are due primarily to their extraordinary ability to inhabit a range of ecological niches and by hosting a variety of symbionts.Attaining relatively large,centimetre-scale sizes,made some forms very specialized and vulnerable to rapid ecological changes.For this reason,some LBF have shown a tendency to suffer periodically during major extinctions,especially when environmental conditions have changed rapidly and/or substantially.This,however,makes them valuable biostratigraphic microfossils and,in addition,gives invaluable insight into the spatial and temporal process of biological evolution,such as convergent/homoplasy and homology/iterative evolution.Here the evolutionary behavior of two important morphological types that occurred throughout the history of the LBF are discussed,namely the planispiral-fusiform test as typified by the fusulinids in the Late Paleozoic and the alveolinids in the Mid-Cretaceous and Neogene,and the three-layered discoid lenticular test as characterized by the orbitoids in the Mid-to Late Cretaceous,the orthophragminids in the Paleogene,and lepidocyclinids in the Oligocene to Quaternary.Understanding the propensity of these forms to convergent and iterative evolution,with the repeated re-occurrence of certain morphological features,is essential in understanding and constructing their phylogenetic relationships more generally within the main groups of the LBF.The insights gained from the history of these LBF have wider implications,and provide a more general understanding of the impacts of climate and ecological changes as driving forces for biological evolution.

ON THE INVARIANT FOR A FAMILY OF DEFORMED HALLEY METHODS

In this paper, an invariant determined by a function used to guarantee the convergence of all members with l ≤ k in the family of deformed Halley iterative methods for solving nonlinear equation in complex field is given. Results include some known ones as this special cases. We get not only the error estimates of the iterative sequences {zn,l} but also those of f(zn,l) for all l ≤ k.