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A Review of Preconditioners for the Interval GaussSeidel Method
, 1991
"... . Interval Newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box X ae R n of a system of nonlinear equations F (X) = 0 with mathematical certainty, even in finiteprecision arithmetic. In such methods, the system ..."
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Cited by 50 (16 self)
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. Interval Newton methods in conjunction with generalized bisection can form the basis of algorithms that find all real roots within a specified box X ae R n of a system of nonlinear equations F (X) = 0 with mathematical certainty, even in finiteprecision arithmetic. In such methods, the system F (X) = 0 is transformed into a linear interval system 0 = F (M) +F 0 (X)( ~ X \Gamma M); if interval arithmetic is then used to bound the solutions of this system, the resulting box ~ X contains all roots of the nonlinear system. We may use the interval GaussSeidel method to find these solution bounds. In order to increase the overall efficiency of the interval Newton / generalized bisection algorithm, the linear interval system is multiplied by a preconditioner matrix Y before the interval GaussSeidel method is applied. Here, we review results we have obtained over the past few years concerning computation of such preconditioners. We emphasize importance and connecting relationships,...
GLOPT  A Program for Constrained Global Optimization
 Developments in Global Optimization
, 1996
"... . GLOPT is a Fortran77 program for global minimization of a blockseparable objective function subject to bound constraints and blockseparable constraints. It finds a nearly globally optimal point that is near a true local minimizer. Unless there are several local minimizers that are nearly global, ..."
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Cited by 15 (7 self)
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. GLOPT is a Fortran77 program for global minimization of a blockseparable objective function subject to bound constraints and blockseparable constraints. It finds a nearly globally optimal point that is near a true local minimizer. Unless there are several local minimizers that are nearly global, we thus find a good approximation to the global minimizer. GLOPT uses a branch and bound technique to split the problem recursively into subproblems that are either eliminated or reduced in their size. This is done by an extensive use of the block separable structure of the optimization problem. In this paper we discuss a new reduction technique for boxes and new ways for generating feasible points of constrained nonlinear programs. These are implemented as the first stage of our GLOPT project. The current implementation of GLOPT uses neither derivatives nor simultaneous information about several constraints. Numerical results are already encouraging. Work on an extension using curvature inf...
Interval methods for certification of the kinematic calibration of parallel robots
 In Proc. IEEE International Conference on Robotics and Automation (ICRA
, 2004
"... Abstract — In this paper, we demonstrate how methods based on interval arithmetic and interval analysis can be used to achieve numerical certification of the kinematic calibration of a parallel robots. We introduce our work by describing the usual calibration methods and the motivations for a numeri ..."
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Cited by 6 (0 self)
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Abstract — In this paper, we demonstrate how methods based on interval arithmetic and interval analysis can be used to achieve numerical certification of the kinematic calibration of a parallel robots. We introduce our work by describing the usual calibration methods and the motivations for a numerical certification. Then, we briefly present the interval methods we used and the kinematic calibration problem. In the main part, we develop our certified approach of this problem in the case of a Gough platform, and we show with numerical examples how this approach avoids wrong solutions produced by classical approach. Details on implementation and performance are also given. I.
Rigorous Computation of Surface Patch Intersection Curves
, 1993
"... A rigorous and efficient algorithm is presented for computing a sequence of points on all the branches of surface patch intersection curves within a given box. In the algorithm, an interval step control continuation method makes certain that the predictor algorithm will not jump from one branch to t ..."
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Cited by 3 (2 self)
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A rigorous and efficient algorithm is presented for computing a sequence of points on all the branches of surface patch intersection curves within a given box. In the algorithm, an interval step control continuation method makes certain that the predictor algorithm will not jump from one branch to the another. These reliability properties are independent of any choice of tuning parameters. Both a 3dimensional box complement method and a containment checking method are able to guarantee that all branches are located. Initial experimental results show that, even with this reliability, the amount of computation is orders of magnitude less than a uniform tesselation of the threedimensional viewing box. Keywords: computational geometry, marching method, continuation method, surface patch intersections, interval computations. 1 Introduction and Notation The goal of this paper is to present general algorithms for computing all surface / surface intersection curves that are mathematically ...
Modelling Of Heat Transfer In Biological Tissue By Interval Fem
 CAMES
"... this paper, an algorithm of calculation of extreme values of temperature based on interval arithmetic is presented. Many mechanical systems with uncertain parameters can be described by parameter dependent system of linear equations K()T=B(). Using natural interval extension of real function, o ..."
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this paper, an algorithm of calculation of extreme values of temperature based on interval arithmetic is presented. Many mechanical systems with uncertain parameters can be described by parameter dependent system of linear equations K()T=B(). Using natural interval extension of real function, one can transform system of linear equation into system of linear interval equation K( )T=B( ). Solution of system of linear interval equations always contains the exact solution of parameter dependent system of equation. This technique is called Interval Finite Element Method. New method of computation of extreme values of mechanical quantities based on monotonicity test is introduced. This method can give exact solution of parameter dependent system of equations. 1
SOME IDEAS TOWARDS GLOBAL OPTIMIZATION OF IMPROVED EFFICIENCY
"... Scope of the talk. The problem is in a rather general form: (P) minimize 0 ( ) x ϕ ..."
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Scope of the talk. The problem is in a rather general form: (P) minimize 0 ( ) x ϕ
Interval Methods for Solving Underdetermined Nonlinear Equations Systems ∗
"... The problem of enclosing all solutions of an underdetermined system of equations is considered. A few variants of the algorithm to solve this problem are compared – some of the features come from the literature and some are original. The paper discusses both implementational and theoretical issues o ..."
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The problem of enclosing all solutions of an underdetermined system of equations is considered. A few variants of the algorithm to solve this problem are compared – some of the features come from the literature and some are original. The paper discusses both implementational and theoretical issues of the problem, including a useful theorem that is proved. Sharedmemory parallelization, using OpenMP is also considered and numerical results for proper test problems are presented.