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This paper deals with novel mathematical methods to locate the edges of heated planar objects employing simple photodiodes. Thereby, both the lateral edge position and the axial distance of the object can be determined. Furthermore, a method which allows the estimation of the rotation angle of the investigated object is discussed. In contrast to an infrared camera, photodiodes and the required electronic components are insensitive to mechanical vibrations commonly experienced in industrial fabrication processes. Nevertheless, the limited spatial resolution of such photodiode ensemble demands for a signal-processing-based resolution enhancement, which is presented in this paper. By means of simulation results, the efficiency of the novel methods is verified. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to study the order of convergence and the efficiency of four families of iterative methods using frozen divided differences. The first two families correspond to a generalization of the secant method and the implementation made by Schmidt and Schwetlick. The other two frozen schemes consist of a generalization of Kurchatov method and an improvement of this method applying the technique used by Schmidt and Schwetlick previously. An approximation of the local convergence order is generated by the examples, and it numerically confirms that the order of the methods is well deduced. Moreover, the computational efficiency indexes of the four algorithms are presented and computed in order to compare their efficiency. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider numerical simulation to a class of constrained dynamic problems where the overall dynamics are determined by the interactions between two sub-systems. We present an iterative algorithm that naturally decouples the computation of the two sub-systems and that ensures an accurate and efficient solution procedure. We conduct rigorous error analysis for the convergence of the iterative algorithm, and verify the analytical results through careful numerical tests. [Copyright &y& Elsevier]

Regularization methods for the solution of ill-posed inverse problems can be successfully applied if a right estimation of the regularization parameter is known. In this paper, we consider the L1-regularized image deblurring problem and evaluate its solution using the iterative forward–backward splitting method. Based on this approach, we propose a new adaptive rule for the estimation of the regularization parameter that, at each iteration, dynamically updates the parameter value, following the evolution of the objective functional. The iterative algorithm automatically stops, without requiring any assumption about the perturbation process, when the parameter has reached a seemingly near optimal value. In spite of the fact that the optimality of this value has not yet been theoretically proved, a large number of numerical experiments confirm that the proposed rule yields restoration results competitive with those of the best state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to find the efficient iterative methods for solving the general matrix equation A1X+ XA2+A3XH+XHA4=B (including Lyapunov and Sylvester matrix equations as special cases) with the unknown complex (reflexive) matrix X. Design/methodology/approach – By applying the principle of hierarchical identification and the Hermitian/skew-Hermitian splitting of the coefficient matrix quadruplet A1; A2; A3; A4 the authors propose a shift-splitting hierarchical identification (SSHI) method to solve the general linear matrix equation A1X+XA2+A3XH+XHA4=B. Also, the proposed algorithm is extended for finding the reflexive solution to this matrix equation. Findings – The authors propose two iterative methods for finding the solution and reflexive solution of the general linear matrix equation, respectively. The proposed algorithms have a simple, neat and elegant structure. The convergence analysis of the methods is also discussed. Some numerical results are given which illustrate the power and effectiveness of the proposed algorithms. Originality/value – So far, several methods have been presented and used for solving the matrix equations by using vec operator and Kronecker product, generalized inverse, generalized singular value decomposition (GSVD) and canonical correlation decomposition (CCD) of matrices. In several cases, it is difficult to find the solutions by using matrix decomposition and generalized inverse. Also vec operator and Kronecker product enlarge the size of the matrix greatly therefore the computations are very expensive in the process of finding solutions. To overcome these complications and drawbacks, by using the hierarchical identification principle and the Hermitian=skew-Hermitian splitting of the coefficient matrix quadruplet (A1; A2; A3; A4), the authors propose SSHI methods for solving the general matrix equation. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose an iterative algorithm to solve large size linear inverse ill posed problems. The regularization problem is formulated as a constrained optimization problem. The dual Lagrangian problem is iteratively solved to compute an approximate solution. Before starting the iterations, the algorithm computes the necessary smoothing parameters and the error tolerances from the data. The numerical experiments performed on test problems show that the algorithm gives good results both in terms of precision and computational efficiency. [Copyright &y& Elsevier]

Abstract: In this paper, the issue of multi-degree reduction of Bézier curves with C 1 and G 2-continuity at the end points of the curve is considered. An iterative method, which is the first of this type, is derived. It is shown that this algorithm converges and can be applied iteratively to get the required accuracy. Some examples and figures are given to demonstrate the efficiency of this method. [Copyright &y& Elsevier]

Abstract: The weighted least-squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition. In this paper, a family of algorithms are applied to solve these problems based on the Kronecker structures. Subsequently, we construct a computationally efficient solutions of coupled restricted singular matrix equations. Furthermore, the need to compute the weighted Drazin and weighted Moore–Penrose inverses; and the use of Tian''s work and Lev-Ari''s results are due to appearance in the solutions of these problems. The several special cases of these problems are also considered which includes the well-known coupled Sylvester matrix equations. Finally, we recover the iterative methods to the weighted case in order to obtain the minimum D-norm G-vector least-squares solutions for the coupled Sylvester matrix equations and the results lead to the least-squares solutions and invertible solutions, as a special case. [Copyright &y& Elsevier]

Many optimization problems reduce to the solution of a system of linear inequalities (SLI). Some solution methods use relaxed, averaged projections. Others invoke surrogate constraints (typically stemming from aggregation). This paper proposes a blend of these two approaches. A novelty comes from introducing as surrogate constraint a halfspace defined by differences of algorithmic iterates. The first iteration is identical to surrogate constraints methods. In next iterations, for a given approximation x¯, besides the violated constraints in x¯, we also take into consideration the surrogate inequality, which we have obtained in the previous iteration. The motivation for this research comes from the recent work of Scolnik et al. (Appl. Numer. Math. 41, 499—513, 2002), who studied some projection methods for a system of linear equations. [ABSTRACT FROM AUTHOR]

Abstract: In this paper two algorithms for computing the principal square root of a centrosymmetric H-matrix with positive diagonal entries are proposed. It is showed that our algorithms ensure significant savings in computational costs, as compared to the case of an arbitrary H-matrix A with positive diagonal entries. [Copyright &y& Elsevier]

It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES(m) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algoritfims for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one. [ABSTRACT FROM AUTHOR]

The paper describes a domain decomposition strategy which allows high efficiency parallel simulations of turbomachinery flows. The implicit ADI parallel solver is based on the scalar approximate factorisation. The Navier-Stokes (NS) and turbulence model equations are discretised by centred finite differences. The results prove that the parallel calculations with domain decomposition, in which each sub-domain explicitly communicates with the adjacent ones at the end of each implicit iteration, may suffer from a considerable deterioration of the convergence rate. A simple sub-iterative domain recoupling strategy allows recovering the convergence rate of a single processor computation. The strategy is carefully analysed and optimised in terms of inter-processor data communication rate and algorithm memory requirements. The span-wise domain decomposition is particularly suited for turbomachinery flows and is applied to a radial impeller and to an axial turbine stator and stage to prove the validity and the accuracy of the proposed approach. The results indicate that the parallel recoupled algorithm usually reach efficiencies of 0.8, with peaks over 0.9 with up to 16 processors, thereby allowing a considerable speed-up of design and verification calculations. [ABSTRACT FROM AUTHOR]

Given convex scattered data in R3 we consider the constrained interpolation problem of finding a smooth, minimal Lp-norm (1 < p < ∞) interpolation network that is convex along the edges of an associated triangulation. In previous work the problem has been reduced to the solution of a nonlinear system of equations. In this paper we formulate and analyse a Newton-type algorithm for solving the corresponding type of systems. The correctness of the application of the proposed method is proved and its superlinear (in some cases quadratic) convergence is shown. Copyright © 2000 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to derive new computable convergence bounds for GMRES. The new bounds depend on the initial guess and are thus conceptually different from standard “worst-case” bounds. Most importantly, approximations to the new bounds can be computed from information generated during the run of a certain GMRES implementation. The approximations allow predictions of how the algorithm will perform. Heuristics for such predictions are given. Numerical experiments illustrate the behavior of the new bounds as well as the use of the heuristics. [ABSTRACT FROM AUTHOR]