arXiv subjects

Glauco Masotti

Publications and source records attributed to Glauco Masotti.

3 recordsLinked to original sources

arXiv2017

An algorithm for minimization of arbitrary generic functions in one dimension over a finite domain

A new algorithm for one-dimensional minimization is described in detail and the results of some tests on practical cases are reported and illustrated. The method requires only punctual computation of the function, and is suitable to be applied in "difficult" cases, that is when the function is highly irregular and has multiple sub-optimal local minima. The algorithm uses quadratic or cubic interpolation and subdivision of intervals in golden ratio as a last resort. It improves over Brent's method and similar ones in several aspects. It manages multiple local minima, takes into account the complications of having to deal with a finite domain, rather than an unlimited one, and has a slightly faster convergence in most cases.

math.OC↗

arXiv2017

A multi-strategy optimizer for arbitrary generic functions in multidimensional space

An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior, irregular and noisy, with steep variations and exhibiting a lot of local sub-optimal points. The complications of having to deal with a finite domain, as this is usually the case, are taken into account. The method is composed of a number of cascaded stages, each employing a different strategy to improve over the results of the previous stage. Many ideas and concepts employed in known methods are re-elaborated in a coherent scheme, plus several new ideas are introduced. Line minimization plays an important role in most stages, for this purpose a new and powerful algorithm for line minimization is used as well.

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arXiv2012

Floating-Point Numbers with Error Estimates (revised)

The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic idea consists of representing FP numbers by means of a data structure collecting value and estimated error information. Under certain constraints, the estimate of the absolute error is accurate and has a compact statistical distribution. By monitoring the estimated relative error during a computation (an ad-hoc definition of relative error has been used), the validity of results can be ensured. The error estimate enables the implementation of robust algorithms, and the detection of ill-conditioned problems. A dynamic extension of number precision, under the control of error estimates, is advocated, in order to compute results within given error bounds. A reduced time penalty could be achieved by a specialized FP processor. The realization of a hardwired processor incorporating the method, with current technology, should not be anymore a problem and would make the practical adoption of the method feasible for most applications.

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