Abstract
In solving parametric sparse linear systems, we want 1) to know relations on parametric coefficients which change the system largely, 2) to express the parametric solution in a concise form suitable for theoretical and numerical analysis, and 3) to find simplified systems which show characteristic features of the system. The block triangularization is a standard technique in solving the sparse linear systems. In this paper, we attack the above problems by introducing a concept of local blocks. The conventional block corresponds to a strongly connected maximal subgraph of the associated directed graph for the coefficient matrix, and our local blocks correspond to strongly connected non-maximal subgraphs. By determining local blocks in a nested way and solving subsystems from low to higher ones, we replace sub-expressions by solver parameters systematically, obtaining the solution in a concise form. Furthermore, we show an idea to form simple systems which show characteristic features of the whole system.
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Work supported in part by Japan Society for the Promotion of Science under Grants 23500003.
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© 2014 Springer International Publishing Switzerland
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Sasaki, T., Inaba, D., Kako, F. (2014). Solving Parametric Sparse Linear Systems by Local Blocking. In: Gerdt, V.P., Koepf, W., Seiler, W.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2014. Lecture Notes in Computer Science, vol 8660. Springer, Cham. https://doi.org/10.1007/978-3-319-10515-4_29
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DOI: https://doi.org/10.1007/978-3-319-10515-4_29
Publisher Name: Springer, Cham
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