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A Levinson-like algorithm for symmetric positive definite semiseparable plus diagonal matrices

In this paper a Levinson-like algorithm is derived for solving symmetric positive definite semiseparable plus diagonal systems of equations. In a first part we solve a Yule-Walker-like system of equations. Based on this O(n) solver an algorithm for a general right-hand side is derived. The new method has a linear complexity and takes 19n − 13 operations. The relation between the algorithm and an upper triangular decomposition of the inverse of the semiseparable plus diagonal matrices is investigated. Numerical experiments are included.