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Computation of Gohberg-Semencul Formulas for a Toeplitz Matrix (1993)
| Content Provider | CiteSeerX |
|---|---|
| Author | Huckle, Thomas |
| Abstract | The inverse of a Toeplitz matrix can be represented in different ways by Gohberg-Semencul formulas as the sum of products of upper and lower triangular Toeplitz matrices. If we have given such a Gohberg-Semencul formula we can solve every equation Tnx = b in O(n log(n)) steps. But we have to decide which linear equations we want to solve in order to get generating vectors for Gohberg-Semencul formulas, which algorithm we want to apply to solve this equations, and what formula we want to use for evaluating T \Gamma1 n b. In this paper we give a full description of all Gohberg-Semencul formulas, and we present and analyse different linear Toeplitz equations for deriving such representations of T \Gamma1 n . Then we look for representations of T \Gamma1 n with special properties in order to guarantee a stable numerical behaviour. Especially we proof that there exists a Gohberg-Semencul formula such that the generating vectors are pairwise orthogonal. Finally, we give a new fast and... |
| File Format | |
| Language | English |
| Publisher Date | 1993-01-01 |
| Access Restriction | Open |
| Subject Keyword | Gohberg-semencul Formula Toeplitz Matrix Generating Vector Equation Tnx Stable Numerical Behaviour Different Way New Fast Linear Equation Analyse Different Linear Toeplitz Equation Full Description Triangular Toeplitz Matrix Special Property |
| Content Type | Text |
| Resource Type | Technical Report |
