Mathematical foundations of computing最新文献

The optimization problems involving local unitary and local contraction matrices and some Hermitian structures have been concedered in this paper. We establish a set of explicit formulas for calculating the maximal and minimal values of the ranks and inertias of the matrices begin{document}$ X_{1}X_{1}^{ast}-P_{1} $end{document}, begin{document}$ X_{2}X_{2}^{ast}-P_{1} $end{document}, begin{document}$ X_{3}X_{3}^{ast}-P_{2} $end{document} and begin{document}$ X_{4}X_{4}^{ast }-P_{2} $end{document}, with respect to begin{document}$ X_{1} $end{document}, begin{document}$ X_{2} $end{document}, begin{document}$ X_{3} $end{document} and begin{document}$ X_{4} $end{document} respectively, where begin{document}$ P_{1}in mathbb{C} ^{n_{1}times n_{1}} $end{document}, begin{document}$ P_{2}in mathbb{C} ^{n_{2}times n_{2}} $end{document} are given, begin{document}$ X_{1} $end{document}, begin{document}$ X_{2} $end{document}, begin{document}$ X_{3} $end{document} and begin{document}$ X_{4} $end{document} are submatrices in a general common solution begin{document}$ X $end{document} to the paire of matrix equations begin{document}$ AX = C $end{document}, begin{document}$ XB = D. $end{document}

The motive of this research article is to introduce a sequence of Szbegin{document}$ acute{a}sz $end{document} Schurer Beta bivariate operators in terms of generalization exponential functions and their approximation properties. Further, preliminaries results and definitions are presented. Moreover, we study existence of convergence with the aid of Korovkin theorem and order of approximation via usual modulus of continuity, Peetre's K-functional, Lipschitz maximal functional. Lastly, approximation properties of these sequences of operators are studied in Bbegin{document}$ ddot{o} $end{document}gel space via mixed modulus of continuity.

In this paper, we study the learning performance of regularized large-margin unified machines (LUMs) for classification problem. The hypothesis space is taken to be a reproducing kernel Hilbert space begin{document}$ {mathcal H}_K $end{document}, and the penalty term is denoted by the norm of the function in begin{document}$ {mathcal H}_K $end{document}. Since the LUM loss functions are differentiable and convex, so the data piling phenomena can be avoided when dealing with the high-dimension low-sample size data. The error analysis of this classification learning machine mainly lies upon the comparison theorem [3] which ensures that the excess classification error can be bounded by the excess generalization error. Under a mild source condition which shows that the minimizer begin{document}$ f_V $end{document} of the generalization error can be approximated by the hypothesis space begin{document}$ {mathcal H}_K $end{document}, and by a leave one out variant technique proposed in [13], satisfying error bound and learning rate about the mean of excess classification error are deduced.

The primary goal of this paper is to present the generalization of begin{document}$ lambda $end{document}-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [24]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.