Abstract
We introduce a generalized Lilbert [Lucas-Hilbert] matrix. Explicit formulæ 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 justification of the necessary identities to the q-version of Zeilberger’s celebrated algorithm.
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Kılıç, E., Prodinger, H. The generalized Lilbert matrix. Period Math Hung 73, 62–72 (2016). https://doi.org/10.1007/s10998-016-0128-1
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DOI: https://doi.org/10.1007/s10998-016-0128-1
Keywords
- Lilbert matrix
- Filbert matrix
- Pilbert matrix
- Fibonacci numbers
- q-Analogues
- LU-decomposition
- Cholesky decomposition
- Zeilberger’s algorithm