A Monotonicity Result for Norms in Conjugate Gradient Algorithms

Anton Schiela ()
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Anton Schiela: Universität Bayreuth

Journal of Optimization Theory and Applications, 2023, vol. 196, issue 1, No 6, 126-146

Abstract: Abstract We show a monotonicity result, enjoyed by norms of iterates of the cg method. It relates the energy norm and the norm, induced by the preconditioner. We place this result into the context of known results and sketch possible applications to ill-posed problems and in unconstrained optimization. Finally, we give some illustration by a numerical example.

Keywords: Conjugate gradients; Quadratic optimization; Monotonicity of norms; 90C06; 65J10; 90C48 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-022-02134-8

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