Computational experiments with ABS algorithms for KKT linear systems

9 M ay 2 00 1 COMPUTATIONAL EXPERIMENTS WITH ABS ALGORITHMS FOR KKT LINEAR SYSTEMS

(A) Let x1 ∈ R n be arbitrary and H1 ∈ R n,n be nonsingular arbitrary. Set i = 1. (B) Compute the residual ri = Axi − b. If ri = 0, then stop, xi solves the problem. Otherwise compute si = HiA T vi, where vi ∈ R n is arbitrary, save that v1, . . . , vi are linearly independent. If si 6= 0, then go to (C). If si = 0 and r T i vi = 0, then set xi+1 = xi, Hi+1 = Hi and go to (F). If si = 0 and r T...

9 M ay 2 00 1 COMPUTATIONAL EXPERIMENTS WITH ABS ALGORITHMS FOR OVERDETERMINED LINEAR SYSTEMS

Abs Algorithms for Linear Equations and Abspack

We present the main results obtained during a research on ABS methods in the framework of the project Analisi Numerica e Matematica Computazionale. 1. – The ABS algorithms. ABS algorithms were introduced by Abaffy, Broyden and Spedicato (1984), to solve linear equations first in the form of the basic ABS class, later generalized as the scaled ABS class and applied to linear least squares, nonli...

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

Exact and approximate solutions of fuzzy LR linear systems: New algorithms using a least squares model and the ABS approach

We present a methodology for characterization and an approach for computing the solutions of fuzzy linear systems with LR fuzzy variables. As solutions, notions of exact and approximate solutions are considered. We transform the fuzzy linear system into a corresponding linear crisp system and a constrained least squares problem. If the corresponding crisp system is incompatible, then the fuzzy ...