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Solving Large Scale Unconstrained Minimization Problems by a New ODE Numerical Integration Method

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DOI: 10.4236/am.2011.25069    4,955 Downloads   8,913 Views   Citations


In reference [1], for large scale nonlinear equations , a new ODE solving method was given. This paper is a continuous work. Here has gradient structure i.e. , is a scalar function. The eigenvalues of the Jacobian of ; or the Hessian of , are all real number. So the new method is very suitable for this structure. For quadratic function the convergence was proved and the spectral radius of iteration matrix was given and compared with traditional method. Examples show for large scale problems (dimension ) the new method is very efficient.

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The authors declare no conflicts of interest.

Cite this paper

T. Han, X. Luo and Y. Han, "Solving Large Scale Unconstrained Minimization Problems by a New ODE Numerical Integration Method," Applied Mathematics, Vol. 2 No. 5, 2011, pp. 527-532. doi: 10.4236/am.2011.25069.


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