By Achim Bachem, Bernhard Korte, Martin Grötschel (auth.), Achim Bachem, Bernhard Korte, Martin Grötschel (eds.)
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Additional info for Mathematical Programming The State of the Art: Bonn 1982
In choosing predictor steps, the following two rules should be observed: 1. Use only information already obtained in order to reduce costly new calculations. 2. Use formulas which are not too sensitive to small variations of the Ui in directions perpendicular to the solution curve, since one may wish to stop the corrector (14) 7 at an early stage in order to save computational costs. A good choice are Adams-Bashforth predictors which are performed with respect to (2). 2]. (17) Solving the linear equations.
Math. : A homotopy method for the calculation of all zeroes of zero-dimensional polynomial ideals. In: Continuation methods, H. ), Academic Press, New York (1978) 69-94 Eaves, B. : Computing Kakutani fixed points. SIAM J. App!. Math. 21 (1971) 236-244 Eaves, B. : Homotopies for computation of fixed points. Math. Programming 3 (1972) 1-22 Eaves, B. : Solving regular piecewise linear convex equations. Math. Programming Study 1 (1974) 96-119 Eaves, B. : Properly labeled simplexes. , G. B. Dantzig, B.
A proof of the nonretractibility of a cell onto its boundary. Proc. Amer. Math. Soc. 14 (1963) 364-365 Hirsch, M. : Differential topology. Springer Verlag, Berlin (1976) Hirsch, M. W. : On algorithms for solving F(x) = O. Comm. Pure and Appl. Math. : Pivotal methods for computing fixed points: a unified approach. Travaux Sem. Anal. Convexe 6 (1978), Exp. no. 20, 35 pp Ikeno, E. : The arc-length method for the computation of characteristic curves. IEEE Transactions on Circuits and Systems Jacovlev, M.