The purpose of this paper is to provide an error analysis for the multicategory support vector machine (MSVM) classificaton problems. We establish the uniform convergency approach for MSVMs and estimate the misclassification error. The main difficulty we overcome here is to bound the offset vector. As a result, we confirm that the MSVM classification algorithm with polynomial kernels is always efficient when the degree of the kernel polynomial is large enough. Finally the rate of convergence and examples are given to demonstrate the main results. [ABSTRACT FROM AUTHOR]
The article strong convergence theorems for approximation of common fixed points for a finite family of pseudocontractive mappings. It states that the approximation of an implicit iteration algorithm are proven in Banach spaces. Mathematicians introduce an implicit iteration process for a family of nonexpensive mappings which is illustrated in mathematical notation. On the other hand, other mathematicians proved the weak convergence of iterative process to a common fixed point of a finite family nonexpansive mappings in a Hilbert space.
Presents a research on the approximation of piecewise polynomial functions in the space c[0,1] by E. D. Livshits. Endowment of research by the Russian Foundation for Basic Research; Notation from Chebyshev on the subject; Theorems on continuous multiplicative selection; Construction of proofs of the theorems which involve metric projection, mathematical equations and functions and banach spaces.