Titlebook: Numerical Continuation Methods; An Introduction Eugene L. Allgower,Kurt Georg Book 1990 Springer-Verlag Berlin Heidelberg 1990 Algorithmus.

obeisance

PL Continuation Methods,urves which could be numerically traced using PC-methods. Now we will discuss piecewise linear (.) methods which can again be viewed as curve tracing methods, but the map . can now be arbitrary. The map . is approximated by a piecewise linear map . which affinely interpolates . at the nodes of a tri

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Delude

General PL Algorithms on PL Manifolds,ted in our bibliography. The PL continuation and homotopy algorithms described in the last two chapters are important examples. In order to give a better idea of the flexibility which is possible and to describe the construction of such algorithms for special purposes, we are now going to cast the n

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Approximating Implicitly Defined Manifolds,which rest rather strongly upon smoothness properties of . and the piecewise-linear methods which require less smoothness, but then on the other hand are generally less flexible as far as allowing general step-lengths is concerned. The latter methods are also no longer viable for large .. The behavi

Modicum

Update Methods and their Numerical Stability,applied when the matrix . is only slightly modified at each subsequent step. This is in particular the case for the update algorithms of chapter 7 and for the PL algorithms of chapters 12–15. As we have noted in those chapters, the modification of . is of the form.where . is some vector of unit leng

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