Many papers have discussed preconditioned block iterative methods for solving full rank least-squares problems. However very few papers studied iterative methods for solving rank-de cient least-squares problems. Miller and Neumann (1987) proposed the 4-block SOR method for solving the rank-de cient problem. Here a 2-block SOR method and a 3-block SOR method are proposed to solve such problem. T...

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...

This paper presents a new 4-points Explicit Group Unsymmetric Successive Overrelaxation (USSOR) iterative method to approximate the solution of the linear systems derived from the discretisation of self-adjoint elliptic partial equations. Several studies have been carried out by many researchers on the USSOR iterative method, for example, the analysis of its convergence [1], an upper bound for ...

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...

The improvement in AOR method for solving this system has been carried out by Hadjimos [1], Recently, Yao-Tang et al. [2], improved AOR method which has been developed by [1]. In this work, we construct a preconditioner to improve the Accelerated Over-relaxation (AOR) iterative method for solution of linear systems. We reduce the spectral radius of iterative matrix by multiplication of Precondi...

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We continue to discuss why MMSE estimation arises in coding schemes that approach the capacity of linear Gaussian channels. Here we consider schemes that involve successive decoding, such as decision-feedback equalization or successive cancellation. “Everything should be made as simple as possible, but not simpler.”— A. Einstein.

Convex relaxations of the power flow equations and, in particular, the Semi-Definite Programming (SDP) and SecondOrder Cone (SOC) relaxations, have attracted significant interest in recent years. The Quadratic Convex (QC) relaxation is a departure from these relaxations in the sense that it imposes constraints to preserve stronger links between the voltage variables through convex envelopes of ...