A curious phenomenon when it comes to solving the linear system formulation of the PageRank problem is that while the convergence rate of Gauss–Seidel shows an improvement over Jacobi by a factor of approximately two, successive overrelaxation (SOR) does not seem to offer a meaningful improvement over Gauss–Seidel. This has been observed experimentally and noted in the literature, but to the be...

Keywords: System of nonlinear integral equations Step method Picard operators Generalized fibre contraction principle a b s t r a c t Using the step method, we study the following system of integral equations from biomathematics xðtÞ ¼ gðt; xðtÞ; xðt À sÞÞ þ Z t tÀs f ðs; xðsÞÞds; t 2 ½a; bŠ; s > 0 and we prove the existence, uniqueness and the convergence of the successive approximation sequen...

This paper covers practical study of responses of the systems which are under control. The auto tune proportional-integral – derivative (PID) controller is used for controlling of systems. The auto tune algorithm is implemented using the successive approximation method. The auto tuner has been checked with various plant models in MATLAB environment that causes only minor perturbation on the nor...

Matrix rank minimization problem is widely applicable in many fields such as control, signal processing and system identification. However, the problem is in general NP-hard, and it is computationally hard to solve directly in practice. In this paper, we provide a new kind of approximation functions for the rank of matrix, and the corresponding approximation problems can be used to approximate ...

Golub et al. (2001, BIT, 41, 71–85) gave a generalized successive over-relaxation method for the augmented systems. In this paper, the connection between the SOR-like method and the preconditioned conjugate gradient (PCG) method for the augmented systems is investigated. It is shown that the PCG method is at least as accurate (fast) as the SOR-like method. Numerical examples demonstrate that th...

This paper presents a new image morphing method using a two-dimensional deformation technique which provides an intuitive model for a warp. The deformation technique derives a C1-continuous and one-to-one warp from a set of point pairs overlaid on two images. The resulting inbetween image precisely reflects the correspondence of features specified by an animator. We also control the transition ...

A new method of successive construction of a solution is developed for problems of strongly nonequilibrium Boltzmann kinetics beyond normal solutions. Firstly, the method provides dynamic equations for any manifold of distributions where one looks for an approximate solution. Secondly, it gives a successive procedure of obtaining corrections to these approximations. The method requires neither ...

This paper presents a new image morphing technique using deformable surfaces. Drawbacks of previous techniques are overcome by a physically-based approach which provides an intuitive model for a warp. A warp is derived by two deformable surfaces which specify horizontal and vertical displacements of points on an image. This paper also considers the control of transition behavior in a metamorpho...

A novel approach to solving the optimal nonlin-ear control problem is presented. Instead of seeking a global approximation to the Hamilton-Jacobi-Bellman equation, a local approximation is obtained by successively solving the Generalized Hamilton-Jacobi-Bellman (GHJB) equation on a local region of the state space. The optimal control is generated by solving the GHJB equation algebraically at se...

Abstract An extension of Boley’s continuum mechanics-based successive approximation method is presented for rectangular beams composed two isotropic linear elastic layers. The solution cast into the form tables, in complete analogy to tables originally by Boley and Tolins single-layer strips. first column these corresponds classical Bernoulli–Euler theory beams. further columns represent compar...