Now showing items 1-6 of 6
The generalized Lilbert matrix
We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formul' are derived for the LU-decomposition and their inverses, as well as the Cholesky decomposition. The approach is to use q-analysis and to leave the ...
The generalized q-Pilbert matrix
(De Gruyter Open Ltd, 2014-10)
A generalized q-Pilbert matrix from[KILIC, E.-PRODINGER, H.: The q-Pilbert matrix, Int. J. Comput. Math. 89 (2012), 1370-1377] is further generalized, introducing one additional parameter. Explicit formul' are derived for ...
A nonsymmetrical matrix and its factorizations
(De Gruyter, 2019-08)
We introduce a nonsymmetric matrix defined by q-integers. Explicit formul ae are derived for its LU-decomposition, the inverse matrices L-1 and U-1 and its inverse. Nonsymmetric variants of the Filbert and Lilbert matrices ...
A nonlinear generalization of the Filbert matrix and its Lucas analogue
(Taylor and Francis Ltd., 2019-01)
In this paper, we present both a new generalization and an analogue of the Filbert matrix (Formula presented.) by the means of the Fibonacci and Lucas numbers whose indices are in nonlinear form (Formula presented.) for ...
New asymmetric generalizations of the Filbert and Lilbert matrices
(Springer Netherlands, 2019-06)
Two new asymmetric generalizations of the Filbert and Lilbert matrices constructed by the products of two Fibonacci and Lucas numbers are considered, with additional parameter settings. Explicit formulæ are derived for ...
New Filbert and Lilbert matrices with asymmetric entries
(De Gruyter, 2020-04)
In this paper, two new analogues of the Hilbert matrix with four-parameters have been introduced. Explicit formulæ are derived for the LU-decompositions and their inverses, and the inverse matrices of these analogue matrices.