On powers of general tridiagonal matrices

Al-Hassan, Qassem M.

doi:10.12988/ams.2015.411900

Cited by 3 publications

(3 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Equation ( 5) requires the computation of the powers of the matrix T n . This is trivial for small values of n whereas, for high matrix orders, the relevant computation can be performed using different algorithms available in the scientific literature such as the ones detailed in [30,31], as well as in [25] for the special case of tridiagonal Toeplitz matrices.…”

Section: The Case Of a Tridiagonal Toeplitz Matrixmentioning

confidence: 99%

Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral

Caratelli

Ricci

2021

Symmetry

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We show that using Dunford-Taylor’s integral, a classical tool of functional analysis, it is possible to derive an expression for the inverse of a general non-singular complex-valued tridiagonal matrix. The special cases of Jacobi’s symmetric and Toeplitz (in particular symmetric Toeplitz) matrices are included. The proposed method does not require the knowledge of the matrix eigenvalues and relies only on the relevant invariants which are determined, in a computationally effective way, by means of a dedicated recursive procedure. The considered technique has been validated through several test cases with the aid of the computer algebra program Mathematica©.

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Section: The Case Of a Tridiagonal Toeplitz Matrixmentioning

confidence: 99%

Inversion of Tridiagonal Matrices Using the Dunford-Taylor’s Integral

Caratelli

Ricci

2021

Symmetry

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“…Without the loss of generality and for simplicity we take n = N 2 , i.e. we consider the distribution of the middle point of the Brownian bridge and in (26) it is supposed that n = N − n > K.…”

Section: B Brownian Bridges and Kpz Statistics On Finite Supertreesmentioning

confidence: 99%

Equilibrium mean-field-like statistical models with KPZ scaling

Gorsky¹,

Nechaev²,

Valov³

2020

Preprint

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“…For example in parallel computing, telecommunication system analysis, solving differential equations using finite differences, heat conduction *Corresponding author: E-mail: m−elmikkawy@yahoo.com and fluid flow problems. The interested reader may refer to ( [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]) and the references therein. (1.2)…”

Section: Introductionmentioning

confidence: 99%