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Complexity bounds for solving some tridiagonal systems with preconditioning

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Abstract

Some special classes of tridiagonal matrices A are considered, and the complexity of solving a linear system Ax=f is investigated, when rational preconditioning on A is allowed. Non-trivial lower bounds are found, and in all cases the number of necessary multiplicative operations, apart from preconditioning, is shown to be greater than the number of indeterminates defining A.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, Corso Italia 40, 56125, Pisa, Italy

    R. Bevilacqua & E. Bozzo

  2. Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Roma, Italy

    G. Temperanza & P. Zellini

Authors
  1. R. Bevilacqua
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  2. E. Bozzo
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  3. G. Temperanza
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  4. P. Zellini
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Bevilacqua, R., Bozzo, E., Temperanza, G. et al. Complexity bounds for solving some tridiagonal systems with preconditioning. Calcolo 30, 127–143 (1993). https://doi.org/10.1007/BF02576177

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  • DOI: https://doi.org/10.1007/BF02576177

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