Department of Computer Science, K.U.Leuven, Leuven, Belgium
TW Reports vol:TW427
In this paper we will derive a solver for a symmetric strongly nonsingular higher order generator representable semiseparable plus band matrix. The solver we will derive is based on the Levinson algorithm, which is used for solving strongly nonsingular Toeplitz systems. In a ﬁrst part an O(p2n) solver for a semiseparable matrix of
semiseparability rank p is derived, and in a second part we derive an O(ln) solver for a band matrix with bandwidth 2l + 1. Both solvers are constructed in a similar way: ﬁrstly a Yule-Walker-like equation needs to be solved, and secondly this solution is used for solving a linear equation with an arbitrary right-hand side.
Finally a combination of the above methods is presented to solve linear systems with semiseparable plus band coeﬃcient matrices. The overall complexity of this solver is 6(l + p)n^2 plus lower order
terms. In a ﬁnal section numerical experiments are performed. Attention is paid to the timing and the accuracy of the described methods.