In the Newton/log-barriermethod,Newton steps are taken for the log-barrier function for a xed value of the barrier parameter until a certain convergence criterion is satis ed. The barrier parameter is then decreased and the Newton process is repeated. A naive analysis indicates that Newton's method does not exhibit superlinear convergence to the minimizer of each instance of the log-barrier fun...

We present several variations, generalizations and extensions of Cauchy's Convergence Criterion for real sequences, including some unusual 2-dimensional versions.

In this paper the convergence criterion of fuzzy random variable is investigated. An attempt is made to study the equivalence relation of uniform integrability of fuzzy random variables. Mean convergence theorem, Lebesgue dominated convergence theorem and Mean Ergodic theorem for the case of fuzzy random variable are introduced.

Hermite subdivision schemes have been studied by Merrien, Dyn and Levin and they appear to be very different from subdivision schemes analyzed before since the rules depend on the subdivision level. As suggested by Dyn and Levin, it is possible to transform the initial scheme into a uniform stationary vector subdivision scheme which can be handled more easily. With this transformation, the stud...

Under the assumption of bounded rationality, economic agents learn from their past mistaken predictions by combining new and old information to form new beliefs. The purpose of this paper is to investigate how the policy-maker, by affecting private agents’ learning process, determines the speed at which the economy converges to the rational expectation equilibrium. I find that by reacting stron...

The convergence of the King-Werner method for finding zeros of nonlinear operators is analyzed. Under the hypothesis that the derivative of f satisfies the radius Lipschitz condition with L-average, the convergence criterion and the convergence ball for the King-Werner method are given. Applying the results to some particular functions L(u), we get the convergence theorems in [7] and [1] as wel...

In this article, a convergence criterion for the Monte Carlo estimates, which can be used as a stopping rule for the Monte Carlo experiments, will be proposed. The proposed criterion seeks a convergence band of a given width and length such that the probability of the Monte Carlo sample means to fall outside of this band is practically null. Although it has some sort of self defined confidence,...