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Titlebook: Numerical Analysis; Proceedings of the 1 David F. Griffiths Conference proceedings 1984 Springer-Verlag Berlin Heidelberg 1984 Analysis.Der

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Some methods for separating stiff components in initial value problems, cost. We develop some methods related to a block Schur factorization of the Jacobian for separating the stiff components. These methods use block versions of the OR or LR algorithm or, for sparse Jacobians, orthogonal iteration to derive an approximate Jacobian. The technique is practical only for
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Nonconvex minimization calculations and the conjugate gradient method,ve function is twice continuously differentiable and has bounded level sets. Most of our attention is given to the Polak-Ribière algorithm, and unfortunately we find examples that show that the calculated gradients can remain bounded away from zero. The examples that have only two variables show als
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Numerical experiments with partially separable optimization problems, motivated by the very large number of minimization problems in many variables having that particular property. The results discussed in the paper cover both unconstrained and bound constrained cases, as well as numerical estimation of gradient vectors. It is shown that exploiting the present underl
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An implicit diffusive numerical procedure for a slightly compressible miscible displacement problemphase miscible displacement problem in a porous medium. This scheme has several desirable features including a substantial reduction of the "grid orientation" effect often observed with other methods. Theoretical convergence analyses for rectangular regions and computational results for this method
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