A NEWTON-RAPHSON VERSION OF THE MULTIVARIATE DYNAMIC ROBBINS-MONRO PROCEDURE | ||||
| International Conference on Aerospace Sciences and Aviation Technology | ||||
| Article 29, Volume 5, ASAT CONFERENCE 4 - 6 May 1993, CAIRO, May 1993, Page 351-358 PDF (1.16 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/asat.1993.25636 | ||||
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| Author | ||||
| El Sayed Sorour | ||||
| Military Technical College, Department of Mathematics. | ||||
| Abstract | ||||
| Let M be a function from Rk to Rk let en, n 1,2,... be (unknown) vector numbers, the first e1 being the unique root of the equation M(g) = 0, set M1(x) = M(x), for n set Mn(x) = M(x - en - el) so that en is the unique toot of Mn(x)-0. Initially Mn(x) is unknown, but for any x in Rk we can observe a random vector Yn(x) with conditional expectation Mn+I(x). The unknown en can be estimated recursively by the author (1978), that procedure requires the rather restrictive assumption that the infiiuum of the inner product over any compact set not containing & be positive, i.e. along each line through el, M(x) is unimodal with minimum el. Unlike our previous method, the procedure introduced in this paper does not necessarily attempt to move in the direction of en but except of that random fluctuations it moves in the direction which decreases (x)112, consequently it does not require that have a constant signum. This new procedure is a stochastic analog of the Newton-Raphson technique. | ||||
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