The University of Niš (Serbian: Универзитет у Нишу, romanized: Univerzitet u Nišu) is a public university in Serbia. It was founded in 1965 and consists of 13 faculties with 1,492 academic staff and around 20,500 students (as of 2018–19 school year). Since its founding, the university diploma has been acquired by more than 50,000 students, including 1,300 foreigners.[citation needed]It has a university library "Nikola Tesla"; the Faculty of Technology is located in Leskovac, Pedagogy Faculty in Vranje and Agriculture Faculty in Kruševac.
The concepts of Moore-Penrose weak Drazin (MP-w-D) and weak Drazin Moore-Penrose (w-D-MP) matrices are defined based on the Moore-Penrose inverse in combination with a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse. By using the mth powers of a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse instead of a minimal rank weak Drazin inverse and a minimal rank right weak Drazin inverse, we generalize the notions of MP-w-D and w-D-MP matrices and present the m-MP-w-D and m-w-D-MP matrices as new classes of square matrices. Recently considered A(dagger )AD, A(D )A dagger, MP-w-D and w-D-MP matrices are special types of m-MP-w-D and m-w-D-MP matrices and we study wider classes of matrices. We verify many characterizations and representations of our new types of matrices. New particular kinds of m-MP-w-D and m-w-D-MP matrices are investigated too. By applying the m-MP-w-D and m-w-D-MP matrices, we solve several linear equations.
Utilizing two different Schur complements, our purpose is to derive new explicit representations of the Moore-Penrose inverse of a 2 x 2 complex block matrix under corresponding hypotheses. By this way, we generalized several known results in the literature. A numerical example is given to illustrate our results.
In this paper, we construct the new iterative method of the form Xk +1 = XkPk(AXk) where Pk is polynomial, for computing the inverse A-1 of a given invertible matrix A is an element of Rnxn. Coefficients of the polynomial Pk in k-th iteration are variable and determined in a way to minimize the Frobenius norm of the error matrix I-AXk+1. The convergence of the new method is investigated, where several theoretical results are proven. The method is compared to the existing iterative methods of the similar type, on a various numerical examples. The results show that the new method outperforms the existing ones for almost all test matrices. Moreover, they suggest that the new method posses almost global convergence. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Let X be an infinite-dimensional complex Banach space and let p be a non-zero complex polynomial. Suppose that T and S are bounded linear operators on X such that T is Koliha-Drazin invertible with finite nullity, p(S) is Riesz and TS=ST. We prove that if pis an odd function and if p(-1)(0) boolean AND sigma(b)(T) subset of {0}, where sigma(b)(T) denotes the Browder spectrum of T, then T + S is Koliha-Drazin invertible. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
In this paper, new improved algorithms for approximate determinization of fuzzy finite automata over the product structure are provided. The algorithms result in fuzzy deterministic and crisp-deterministic fuzzy automata whose fuzzy languages differ from the fuzzy language of the original automaton only for those words that are accepted in the original automaton with a degree lower than the prescribed value, and the difference is also smaller than that prescribed value. In addition, the algorithms produce fuzzy automata that are minimal in the class of all fuzzy automata whose language differs from the original one by less than that prescribed value. Compared with other algorithms for approximate determinization, the proposed algorithms show better efficiency, because the improvement based on the use of approximate weak simulations can significantly reduce the number of intermediate states in the first phase of algorithm implementation.
