2 results
1 - Linear Operators and Matrices
- from Part I - Numerical Linear Algebra
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- Book:
- Classical Numerical Analysis
- Published online:
- 29 September 2022
- Print publication:
- 20 October 2022, pp 3-19
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MATRIX ANALYSES ON THE DAI–LIAO CONJUGATE GRADIENT METHOD
- Part of
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- Journal:
- The ANZIAM Journal / Volume 61 / Issue 2 / April 2019
- Published online by Cambridge University Press:
- 09 May 2019, pp. 195-203
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- Article
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Some optimal choices for a parameter of the Dai–Liao conjugate gradient method are proposed by conducting matrix analyses of the method. More precisely, first the
$\ell _{1}$ and 
$\ell _{\infty }$ norm condition numbers of the search direction matrix are minimized, yielding two adaptive choices for the Dai–Liao parameter. Then we show that a recent formula for computing this parameter which guarantees the descent property can be considered as a minimizer of the spectral condition number as well as the well-known measure function for a symmetrized version of the search direction matrix. Brief convergence analyses are also carried out. Finally, some numerical experiments on a set of test problems related to constrained and unconstrained testing environment, are conducted using a well-known performance profile.
