A Tridiagonalization Method for Symmetric Saddle-Point Systems

Alfredo Buttari 1 Dominique Orban 2 Daniel Ruiz 1 David Titley-Peloquin 3
1 IRIT - Institut de recherche en informatique de Toulouse
2 GERAD
3 Université McGill
Abstract : We propose an iterative method for the solution of symmetric saddle-point systems that exploits the orthogonal tridiagonalization method of Saunders, Simon, and Yip (1988). By contrast with methods based on the Golub and Kahan (1965) bidiagonalization process, our method takes advantage of two initial vectors and splits the system into the sum of a least-squares and a least-norm problem. Our method typically requires fewer operator-vector products than MINRES, yet performs a comparable amount of work per iteration and has comparable storage requirements.
Keywords : Symmetric saddle-point systems iterative methods orthogonal tridiagonalization
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Alfredo Buttari, Dominique Orban, Daniel Ruiz, David Titley-Peloquin. A Tridiagonalization Method for Symmetric Saddle-Point Systems. SIAM Journal on Scientific Computing, Society for Industrial and Applied Mathematics, 2019, 41 (5), pp.S409-S432. ⟨10.1137/18M1194900⟩. ⟨hal-02343661⟩

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