Alireza Ataei

Alireza Ataei
Persian Gulf University | PGU · Department of Mathematics

PhD

About

6
Publications
1,362
Reads
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61
Citations
Citations since 2017
1 Research Item
31 Citations
201720182019202020212022202302468
201720182019202020212022202302468
201720182019202020212022202302468
201720182019202020212022202302468
Introduction

Publications

Publications (6)
Article
Full-text available
The energy of a graph G is equal to the sum of the absolute values of the eigenvalues of G , which in turn is equal to the sum of the singular values of the adjacency matrix of G. Let X, Y and Z be matrices, such that X+Y= Z. The Ky Fan theorem establishes an inequality between the sum of the singular values of Z and the sum of the sum of the singu...
Article
Full-text available
The energy of a graph $G$ is equal to the sum of the absolute values of the eigenvalues of $G$ , which in turn is equal to the sum of the singular values of the adjacency matrix of $G$. Let $X$, $Y$ and $Z$ be matrices, such that $X+Y= Z$. The Ky Fan theorem establishes an inequality between the sum of the singular values of $Z$ and the sum of the...
Article
Full-text available
Katsikis et al. presented a computational method in order to calculate the Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) (2011). In this paper, an improved version of this method is presented for computing the pseudo inverse of an m × n real matrix A with rank r > 0 . Numerical experiments show that the resul...
Article
The Moore–Penrose inverse of an arbitrary matrix (including singular and rectangular) has many applications in statistics, prediction theory, control system analysis, curve fitting and numerical analysis. In this paper, an algorithm based on the conjugate Gram–Schmidt process and the Moore–Penrose inverse of partitioned matrices is proposed for com...

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Projects

Projects (2)
Project
ISEDS at Persian Gulf University (PGU) has pioneered many of the tools and ideas behind the research and applications often classified as "intelligent systems" and “data science,” where computer science, electrical engineering, statistics, and mathematics join together. This Faculty sees an even brighter future for data science as it harnesses a wider set of ideas to build a new more subtle and powerful science of data. As well as being interested in prediction and statistical computation, our Faculty puts equal weight on designing experiments, modeling sophisticated dependencies (networks, data streams), and trying to understand and quantify causal mechanisms, not simply averages and associations, with large data sets. These views are reflected in our curriculum targeted to data science specialists, our faculty’s research, and the work of our research students.
Project
Partial least squares is a common technique for multivariate regression. In this project, a linear model is fitted by projection into the span of the basis vectors for the explaining variables and the solution vectors.