Gmres-type Methods for Inconsistent Systems
نویسنده
چکیده
Throughout this paper the integer l is defined by (1.3). Saad and Schulz [6, Proposition 2] show that when A is nonsingular and m ≥ l, the solution xm of the minimization problem (1.2) solves the linear system (1.1). The GMRES method is often implemented by first computing an orthogonal basis {vj} min{m,l} j=1 of the Krylov subspace Km(A, r0) by Arnoldi’s method; see Saad [7] or Saad and Schultz [6]. Let k = min{m, l}. Arnoldi’s method yields the decomposition
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