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Abstract
The method of conjugate gradients (CG) is widely used for the iterative solution of large sparse systems of equations Ax=b, where A is symmetric positive definite. Let xk denote the kth iterate of CG. In this paper we obtain an expression for Jk, the Jacobian matrix of xk with respect to b. We use this expression to obtain computable bounds on the spectral norm condition number of xk, and to design algorithms to compute or estimate Jk.v and JkT.v for a given vector v. We also discuss several applications in which these ideas may be used. Numerical experiments are performed to illustrate the theory.
Original language  English 

Pages (fromto)  110126 
Journal  SIAM Journal on Matrix Analysis and Applications 
Volume  35 
Issue number  1 
Early online date  14 Feb 2014 
DOIs  
Publication status  Published  2014 
Keywords
 linear algebra
 conjugate gradients
 sesnistivity analysis
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Projects
 1 Active
Activities

A primaldual approach of weakconstrained variational data assimilation: (Iterate) History matters
Philippe Toint (Speaker)
13 Oct 2017Activity: Talk or presentation types › Invited talk

Data Assimilation for Weather Forecasting: Reducing the Curse of Dimensionality
Philippe Toint (Invited speaker)
1 Dec 2015Activity: Talk or presentation types › Oral presentation

Oxford University
Philippe Toint (Visiting researcher)
14 Nov 2013 → 17 Nov 2013Activity: Visiting an external institution types › Research/Teaching in a external institution