حل عددی یک مدل انتگرالی بلک شولز با استفاده از یک روش جدید مبتنی بر توابع پایهای شعاعی و تفاضلات متناهی فشرده
Nushin Shahrokhi * , Somaye Arabi Naree Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Received: 2018/10/09 Accepted: 2019/10/28 Paper pages (111-126) Abstract Nonnegative Matrix Factorization is a new approach to reduce data dimensions. In this method, by applying the nonnegativity of the matrix data, the matrix is decomposed into components that are more interrelated and divide the data into sections where the data in these sections have a specific relationship. In this paper, we use the nonnegative matrix factorization to decompose the user ratings matrix in recommender systems. The user ratings matrix is factorized in a way that the users with similar interests can be identified. In this paper, we used a regularization method to minimize the difference between the main matrix and the factorized components. To this end we insert the coefficients which are defined as the norm of the decomposition factors in the factorization equation. The coefficients control the entries of the decomposition factors in a multiplication update process. Our numerical results on the MovieLens data set represent the greater accuracy of our proposed method in predicting user ratings for items.
Grobner basis with respect to several orderings is a powerful tool to compute multivariate difference dimension polynomials. In this paper, an algorithm for computing a Grobner basis of a difference module over a ground difference field with respect to several term orderings is presented. In this direction, a representation of an element of a difference module with respect to several term orderings is introduced. Based on such representation, we generalize the Buchberger theorem to the case of free modules over difference rings with several term orderings associated with a partition of the set of variables. Furthermore, the necessary and sufficient condition is given for the existence of a Grobner basis with respect to several term orderings. In the sequel, we present our implementation of the algorithm on Maple. ./files/site1/files/%D8%AD%D8%B1%D9%81_%D8%B4%D9%86%D9%88%D8%A8%D8%B5%DB%8C%D8%B1%DB%8C(1).pdf
Solving Special Case of Inverse Sturm-Liouville Problem with Aftereffect by using Chebyshev Polynomials
