Algorithm 1 An algorithm for solving \(L{\bf{s}}={\bf{t}}\).

From: Two fast algorithms for finding the solution of the lower Hessenberg quasi-Toeplitz linear system from Markov chain

   Step 1: Solve \(T\varrho = \eta\) and \(T\varsigma = {\bf{t}}\) by using fast Toeplitz solver.

   Step 2: Output the solution vector: \({\bf{s}}=\varsigma -\frac{\varsigma _1}{1+\varrho _1}\varrho\).

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