Explicit inverse of symmetric, tridiagonal near Toeplitz matrices with strictly diagonally dominant Toeplitz part

Abstract

Abstract Let T n = tridiag ( − 1 , b , − 1 ) {T}_{n}={\rm{tridiag}}\left(-1,b,-1) , an n × n n\times n symmetric, strictly diagonally dominant tridiagonal matrix ( ∣ b ∣ > 2 | b| \gt 2 ). This article investigates tridiagonal near-Toeplitz matrices T ˜ n ≔ [ t ˜ i , j ] {\widetilde{T}}_{n}:= \left[{\widetilde{t}}_{i,j}] , obtained by perturbing the ( 1 , 1 ) \left(1,1) and ( n , n ) \left(n,n) entry of T n {T}_{n} . Let t ˜ 1 , 1 = t ˜ n , n = b

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