The spectral analysis of random recurrence systems of growing dimension is considered, when the number of entries (parameters or coefficients) of matrices and the number of their observations have the same order. We develop a random matrix language for a problem of finding the limit spectra of the product of random matrices (matriciant) on the basis of axioms of general statistical analysis (GSA), V.I.C.T.O.R.I.A.-function (Very Important Calculative Transformation of Randomly Independent (Invisible, etc.) Arrays), REFORM method (Resolvents Formulas for Martingales), etc.
A perturbation method is proposed for solving some minimax control problems. The method is based on perturbation of eigenvalues of linear operators in a Hilbert space and Raleigh formulas. An explicit solution of the control problem under uncertainty is obtained.Let ~(t) be a n-dimensional real vector function that solves the equation(1) dt where A(t), B(t) are appropriately dimensioned matrices with continuous elements on [t o, tl]; ~(t) is the control vector function with continuous components on [t o, q]; T is a vector from the space Rn: its magnitude is undefined and we only know that it takes values from some set G = {t', (~', t') __. 1 }. The control is sought in the form ~ = K(t)~(t), where K(t) is an unknown matrix.Consider the functional |t) IEC to where Qo, QI(t) are nonnegative definite matrices, Q2(t) is a positive definite matrix, and Ql(t) and Q2(t) have continuous elements on [t o, tl]. The minimax controller is sought from the condition d (Ko) = inf I (K). K THEOREM.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.