A note on representations for the inverses of tridiagonal matrices |
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| Authors: | J Abderramán Marrero M Rachidi |
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| Institution: | 1. Department of Mathematics Applied to Information Technologies , (ETSIT?-?UPM) Telecommunication Engineering School, Technical University of Madrid , Avda. Complutense s/n. Ciudad Universitaria, 28040 Madrid , Spain jc.abderraman@upm.es;3. Group DEFA – Department of Mathematics and Informatics, Faculty of Sciences , University Moulay Ismail , B.P. 4010, Beni M'hamed , Meknes, Morocco |
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| Abstract: | In this note, we propose an explicit representation with the nested sums for the entries of the inverses of general tridiagonal nonsingular matrices. Its equivalence with other particular representations, based on the combinatorial expressions or the continued fractions, is considered. In addition, an analytical representation for the entries of the finite sections of the resolvent of Jacobi matrices, in terms of its related orthogonal polynomials, is observed. |
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| Keywords: | continued fraction difference equation inverse matrix Jacobi matrix nested sum tridiagonal matrix |
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