Groupe d’études et de recherche en analyse des décisions

G-2018-42

A tridiagonalization method for symmetric saddle-point and quasi-definite systems

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We propose an iterative method for the solution of symmetric saddle-point and quasi-definite 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.

, 22 pages