A unidimensional convergence test for matrix iterative processes applied to Strapdown Navigation

The investigation of the convergence properties of matrix iterative processes usually involves test matrices of high order. This fact may prohibit an analytic approach to the problem. In this paper a method is presented which converts the multidimensional test procedure into a scalar one. The method is presented in conjunction with the problem of matrix orthogonalization which exists in Strapdown Inertial Navigation. Three examples are presented in which the convergence of matrix orthogonalization techniques is investigated. The examples demonstrate the use of the unidimensional convergence test in determining the order of the processes and in finding sufficient conditions for convergence. Numerical results are presented.     

Accelerating the convergence of iterative error correction algorithms for measuring instruments

Translated from Izmeritel'naya Tekhnika, No. 1, pp. 21–23, January, 1989.     

Phase-space representation of iterative design processes

A large variety of design optimization methods have been proposed in recent years. Comparison of the relative performance of each method is a difficult task, and attempts to do so are often based on a limited number of numerical experiments. Recently, a ‘basins of attraction’ construction has been proposed as a graphical tool for investigating global performance of iterative design optimization methods, and as a basis for comparison of different methods. The phase-space representation presented in this paper is a companion to the basins of attraction construction. Basins of attraction reveal the relationship between starting design and final outcome of the solution process; the phase-space construction reveals that nature of the paths connecting the starting design and final outcome. The two constructions complement one another in summarizing the performance of design optimization processes. Both constructions are demonstrated in this paper, applied to the optimal design of an elastic grillage structure using Newton's method and the stress ratio method.     

The convergence behaviour of iterative methods on severely stretched grids

In this paper we examine the dramatic influence that a severe stretching of finite difference grids can have on the convergence behaviour of iterative methods. For the most important classes of iterative methods this phenomenon is considered for a simple model problem with various boundary conditions and an exponential grid. It is shown that grid compression near 2 Neumann boundary or in the centre can make the convergence of some methods extremely slow, whereas grid compression near a Dirichlet boundary can be very advantageous. More theoretical insight is obtained by analysing the spectrum of the Jacob: matrix for one- and two-dimensional problems. Several bounds on dominant eigenvalues of this matrix are given. The final conclusions are also applicable to problems with a variable diffusion coefficient and convection-diffusion equations solved by central difference schemes.     

On the convergence of iterative solutions of the integral magnetic field equation

The solution of the integral magnetic field equation by numerical iteration is discussed. Using a simple linear example, it is shown rigorously that relaxation techniques are required to obtain convergence. The range of permissible relaxation parameters is examined and that particular value which yields most rapid convergence is determined. An iterative solution to a simple nonlinear problem is shown to converge rapidly if the relaxation parameter is adjusted appropriately at each step in the iteration. For the general case of a saturable media of complex geometric shape, a relaxation matrix method is proposed in order to achieve rapid convergence.     

Improvements of convergence characteristics of Newton-Raphsonmethod for nonlinear magnetic field analysis

In order to overcome the divergence of the Newton-Raphson iteration in the nonlinear magnetic field analysis, a relaxation factor is introduced and its optimum value is examined. It is shown that the modified Newton-Raphson method proposed exhibits quick and successful convergence even in the case when the conventional Newton-Raphson method fails in convergence     

针对一类高阶迭代学习控制算法收敛速度的研究

对于单输入单输出系统的P型学习律的收敛问题,文献[1]讨论了一阶、二阶P型学习律的收敛速度,证明了一阶P型学习律比二阶P型学习律的收敛速度快.对于三阶、三阶以上的P型学习律的收敛速度却少有文献研究.文章解决了三阶P型迭代学习控制算法的最优收敛速度问题.     

Parametric estimation of local characteristics for Markov diffusion processes

A method is presented for the parametric estimation of drift and diffusion coefficients for a Markov diffusion process simulating the behavior of a complicated mechanical system for use in computational procedures in intelligent data-acquisition systems. __________ Translated from Izmeritel’naya Tekhnika, No. 12, pp. 15–17, December, 2005.     

Asymptotic rates of convergence of iterative methods applied to finite difference calculations on non-uniform grids

In this paper the use of strongly stretched finite difference grids is examined in detail for a simple model equation. Numerical solutions of this equation demonstrate the overall second-order accuracy of the difference approximations. The behaviour of two simple iterative methods, S.O.R. and stationary A.D.I. is discussed for several cases with strong grid stretching and with variable diffusion coefficients. The results show that grid compression near to boundaries can greatly enhance the rates of convergence of these iterative methods, whereas with grid compression in the centre the rate of convergence can be extremely slow. The case of a diffusion coefficient which increases away from the boundaries of a region is analogous to grid compression in the centre and again the convergence rates can degrade considerably.     

Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms

Numerous situations in continuum mechanics, structural stability, optimization and related fields generate problems requiring the solution of nonlinear algebraic equations. To solve such problems, a large assortment of schemes has evolved over the years. This paper will consider the formal numerical properties of the newly developed constrained type incremental Newton-Raphson operator schemes. Specifically the evaluation of the formal behavior of the elliptically constrained version is treated in detail. Note this procedure has the versatility to efficiently handle a wide range of nonlinearities including the possibilities of positive, negative, semi and indefinite tangent properties in an inherently stable manner. The formalism includes such items as determining from both a global as well as local point of view the existence, uniqueness and convergence characteristics. Also included in the developments will be the determination of the occurrence of global safety zones wherein convergence is assured. The approach taken is general enough to provide a framework to enable applications to a wide variety of constrained schemes involving continuous, piecewise continuous, closed or open constraint conditions.     

Measuring production yield for processes with multiple quality characteristics

Process yield is an important criterion used in the manufacturing industry for measuring process performance. Methods for measuring yield for processes with single characteristic have been investigated extensively. However, methods for measuring yield for processes with multiple characteristics have been comparatively neglected. In this paper, we develop a generalized yield index, called TS _pk,PC , based on the index S_pk introduced by Boyles (Journal of Quality Technology, 23, 17–26, 1991 Boyles, RA. 1991. The Taguchi capability index. J. Qual. Technol., 23: 17–26. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) using the principal component analysis (PCA) technique. We obtained a lower confidence bound (LCB) for the true process yield. The proposed method can be used to determine whether a process meets the preset yield requirement, and make reliable decisions. Examples are provided to demonstrate the proposed methodology.     

An improved self-consistent phonon approximation including four-phonon processes

An improved self-consistent phonon theory (ISC) including three- and four-phonon processes has been used to calculate the zero-pressure lattice parameters and the zero-pressure thermal expansion for Kr. The results indicate that, however limited ISC theory with three-phonon processes may be, trying to supplement this theory with higher-order phonon terms will make the convergence of the theory less satisfactory. In the light of our results we discuss earlier related work as well as a paper by Van Doren and Henkel.     

Vanadium oxide films with improved characteristics for ir microbolometric matrices

Vanadium oxide (VO_x) films intended for use in uncooled IR microbolometric matrices were deposited by reactive magnetron sputtering on silicon substrates. Optimum deposition conditions were determined, which provide for the obtaining of films possessing a current 1/f noise level 3–10 times lower, extended dynamic range, and increased working temperature interval. It was found that the 1/f noise level of the VO_x films depends on the VO₂ phase content and grain size. It is suggested that the observed 1/f noise is caused by the martensite transformation characteristic of the semiconductor-metal phase transition in VO₂.     

Ultra-wideband antenna with improved gain characteristics

A ultra-wideband (UWB) antenna with improved gain characteristics is proposed. With the improvements, it is discussed in terms of the band notch and enhanced radiation patterns. Shaping the return loss as an approach in order to achieve these characteristics is introduced and a multi-resonant dipole structure is designed and experimented in frequency and time domains. The proposed UWB antenna provides the band notch with a sharp slope and improved gain deviation on azimuth plane for the UWB communication.     

Fast convergence with spectral volume integral equation for crossed block-shaped gratings with improved material interface conditions

For block-shaped dielectric gratings with two-dimensional periodicity, a spectral-domain volume integral equation is derived in which explicit Fourier factorization rules are employed. The Fourier factorization rules are derived from a projection-operator framework and enhance the numerical accuracy of the method, while maintaining a low computational complexity of O(NlogN) or better and a low memory demand of O(N).