Several Explicit and Recurrent Formulas for Determinants of Tridiagonal Matrices via Generalized Continued Fractions

Abstract

In the paper, by the aid of mathematical induction and some properties of determinants, the authors present several explicit and recurrent formulas of evaluations for determinants of general tridiagonal matrices in terms of finite generalized continued fractions and apply these newly-established formulas to evaluations for determinants of the Sylvester matrix and two Sylvester type matrices.

Computing sums in terms of beta, polygamma, and Gauss hypergeometric functions

“…Theorem 2.2 in [19] reads that the determinant |P n | of the tridiagonal matrix P n for n ≥ 2 can be computed explicitly by…”

A Hybrid Numerical Algorithm for Evaluating n-th Order Tridiagonal Determinants

“…These matrices arise frequently in a wide range of scientific and engineering fields [3,4,5,6]. For instance, telecommunication, parallel computing, and statistics.…”