Reduction to Hessenberg form is a major performance bottleneck in the computation of the eigenvalues of a nonsymmetric matrix; which takes O(N 3) flops. All the known blocked and unblocked direct Hessenberg reduction algorithms have an I/O complexity of O(N3/B). To improve the performance by incorporating matrix-matrix operations in the computation, usually the Hessenberg reduction is computed in two steps: the first reducing the matrix to a banded Hessenberg form, and the second further reducing it to Hessenberg form. We propose and analyse the first step of the reduction, i.e., reduction of a nonsymmetric matrix to banded Hessenberg form of bandwidth t for varying values of N and M (the size of the internal memory), on external memory model introduced by Aggarwal and Vitter for the I/O complexity and show that the reduction can be performed in O(N3 / min{t,√ M}B) I/Os. © Springer-Verlag 2012.
CITATION STYLE
Mohanty, S. K., & Sajith, G. (2012). I/O efficient algorithms for block hessenberg reduction using panel approach. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7678 LNCS, pp. 134–147). https://doi.org/10.1007/978-3-642-35542-4_12
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