Variable metric method with limited storage for large-scale unconstrained minimization

Ladislav Lukšan

Displaying similar documents to “Variable metric method with limited storage for large-scale unconstrained minimization”

Combining the preconditioned conjugate gradient method and a matrix iterative method

Jan Zítko (1996)

Applications of Mathematics

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The preconditioned conjugate gradient method for solving the system of linear algebraic equations with a positive definite matrix is investigated. The initial approximation for conjugate gradient is constructed as a result of a matrix iteration method after $m$ steps. The behaviour of the error vector for such a combined method is studied and special numerical tests and conclusions are made.

Efficient trust region method for nonlinear least squares

Ladislav Lukšan (1996)

Kybernetika

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Conjugate gradient algorithms for conic functions

Ladislav Lukšan (1986)

Aplikace matematiky

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The paper contains a description and an analysis of two modifications of the conjugate gradient method for unconstrained minimization which find a minimum of the conic function after a finite number of steps. Moreover, further extension of the conjugate gradient method is given which is based on a more general class of the model functions.