Abstract
The local regularization method for solving the first-order numerical differentiation problem is considered in this paper. The a-priori and a-posteriori selection strategy of the regularization parameter is introduced, and the convergence rate of local regularization solution under some assumption of the exact derivative is also given. Numerical comparison experiments show that the local regularization method can reflect sharp variations and oscillations of the exact derivative while suppress the noise of the given data effectively.
Highlights
Let be a Lie algebra of all matrices of order
We work with finite-dimensional modules and finite-dimensional representation of
Choose integers, such that the inequality is satisfied. These partitions are quite important because they appear to be the core in constructing representations. These chosen integers are used to construct some index set
Summary
Let be a Lie algebra of all matrices of order. In this paper, we work with finite-dimensional modules and finite-dimensional representation of. Choose integers , , , such that the inequality is satisfied These partitions are quite important because they appear to be the core in constructing representations. L. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of. Tsetlin gave an explicit construction of a basis for every simple finitedimensional module of In their work, they gave all the irreducible representations of general linear algebra ( ). E. Ramirez provided a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra [2]. This paper will show that the Gelfand-Tsetlin constructions given in the year [1] forms all the irreducible representations of special linear algebra by providing proofs to results.
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