In this paper we present new formulas for characterizing the sensitivity of tridiagonal systems that are independent of the condition number of the underlying matrix. We also introduce efficient algorithms for solving tridiagonal systems of linear equations which are stable and reliable (namely, stable in the backward sense and little sensitive to perturbations in the coefficients).
Reliable Solution of Tridiagonal Systems of Linear Equations / I., BAR ON; Leoncini, Mauro. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - STAMPA. - 38:4(2000), pp. 1134-1153. [10.1137/S0036142998347991]
Reliable Solution of Tridiagonal Systems of Linear Equations
LEONCINI, Mauro
2000
Abstract
In this paper we present new formulas for characterizing the sensitivity of tridiagonal systems that are independent of the condition number of the underlying matrix. We also introduce efficient algorithms for solving tridiagonal systems of linear equations which are stable and reliable (namely, stable in the backward sense and little sensitive to perturbations in the coefficients).
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