We present a uniform description of sets of
m
linear forms in
n
variables over the field of rational numbers whose computation requires
m
(
n
– 1) additions.
This paper presents the construction of a new family of explicit schemes for the numerical solution of initial-value problems of ordinary differential equations (ODEs). The one-parameter family is ...constructed by considering a suitable rational approximation to the theoretical solution, resulting a family with second-order convergence and A-stable. Imposing that the principal term in the local truncation error vanishes, we obtain an expression for the parameter value in terms of the point (xn, yn) on each step. With this approach, the resulting method has third order convergence maintaining the characteristic of A-stability. Finally, combining this last method with other of order two in order to get an estimation for the local truncation error, an implementation in variable step-size has been considered. The proposed method can be used in a wide range of problems, for solving numerically a scalar ODE or a system of first order ODEs. Several numerical examples are given to illustrate the efficiency and performance of the proposed method in comparison with some existing methods in the literature.
In this study a new algorithm is proposed for distributed blind sensor macro-calibration in networked control systems robust to noise. The proposed distributed algorithm for estimation of gain and ...offset correction parameters is of stochastic approximation type, with local non-linear transformations of residuals. Convergence of the algorithm in mean-square and with probability one to consensus is proved for a large class of non-linear transformations, network properties and communication and measurement noise characteristics. The choice of the introduced non-linear transformations in accordance with the theory of robust statistics leads to the proposal of new calibration algorithms robustified w.r.t. noise. It is demonstrated by Monte Carlo simulation that the proposed algorithms are very efficient in the presence of large outliers from the point of view of both achievement of high convergence rate and adequate values of convergence points, outperforming the existing linear algorithms.
In the framework of Zhuravlev’s algebraic approach to classification problems, a linear model of algorithms is investigated (estimates of class membership are generated by linear regressions). The ...possibility of weakening the completeness requirement (obtaining an arbitrary estimation matrix) in order to obtain any classification of a fixed set of objects by using special decision rules is investigated.
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