@incollection{GroetschelWakabayashi1990, author = {Gr{\"o}tschel, Martin and Wakabayashi, Yoshiko}, title = {Composition of facets of the clique partitioning polytope}, booktitle = {Topics in combinatorics and graph theory. Essays in honour of Gerhard Ringel}, editor = {Bodendiek, Rainer and Henn, Rudolf}, publisher = {Physica-Verlag}, address = {Heidelberg}, pages = {271 -- 284}, year = {1990}, language = {en} } @article{GroetschelWakabayashi1990, author = {Gr{\"o}tschel, Martin and Wakabayashi, Yoshiko}, title = {Facets of the clique partitioning polytope}, volume = {47}, journal = {Mathematical Programming, Series A}, number = {3}, pages = {367 -- 387}, year = {1990}, language = {en} } @article{GroetschelMonma1990, author = {Gr{\"o}tschel, Martin and Monma, Clyde}, title = {Integer Polyhedra Arising from Certain Network Design Problems with Connectivity Constraints}, volume = {3}, journal = {SIAM Journal on Discrete Mathematics}, number = {4}, pages = {502 -- 523}, year = {1990}, language = {en} } @inproceedings{AscheuerEscuderoGroetscheletal.1990, author = {Ascheuer, Norbert and Escudero, Laureano and Gr{\"o}tschel, Martin and Stoer, Mechthild}, title = {On Identifying in Polynomial Time Violated Subtour Elimination and Precedence Forcing Constraints for the Sequential Ordering Problem}, booktitle = {Integer Programming and Combinatorial Optimization, Proceeedings of a Conference held at the University of Waterloo, May 28-30, 1990}, editor = {Kannan, Ravi and Pulleyblank, William}, publisher = {University of Waterloo Press}, pages = {19 -- 28}, year = {1990}, language = {en} } @article{Schmidt1990, author = {Schmidt, Frank}, title = {Simulation und Herstellung von Faserschleifkopplern}, volume = {39}, journal = {Wissenschaftliche Zeitschrift der Humboldt-Universit{\"a}t zu Berlin, R. Math./Naturwiss.}, number = {2}, pages = {115 -- 118}, year = {1990}, language = {en} } @article{DeuflhardNowakWulkow1990, author = {Deuflhard, Peter and Nowak, Ulrich and Wulkow, Michael}, title = {Recent Developments in Chemical Computing}, volume = {14}, journal = {Computers in Chemical Engineering}, pages = {1249 -- 1258}, year = {1990}, language = {en} } @article{DeuflhardFreundWalter1990, author = {Deuflhard, Peter and Freund, R. and Walter, Artur}, title = {Fast secant methods for the iterative solution of large nonsymmetric linear systems}, volume = {2}, journal = {IMPACT Comput. Sci. Eng.}, pages = {244 -- 276}, year = {1990}, language = {en} } @inproceedings{Deuflhard1990, author = {Deuflhard, Peter}, title = {Uniqueness Theorems for Stiff ODE Initial Value Problems}, booktitle = {Numerical analysis 1989, proceedings 13th Biennial Conference on Numerical Analysis 1989,}, editor = {Griffiths, D. and Watson, G.}, publisher = {Dundee, Longman Scientific \& Technical, Harlow, Essex, UK,}, pages = {74 -- 205}, year = {1990}, language = {en} } @misc{Walter1990, author = {Walter, Artur}, title = {Sparse Secant Methods for the Iterative Solution of Large Nonsymmetric Linear Systems.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-483}, number = {SC-90-20}, year = {1990}, abstract = {A variety of secant methods has been revisited in view of the construction of iterative solvers for large nonsymmetric linear systems \$ Ax = b \$ stemming from the discretization of convection diffusion equations. In the first section, we tried to approximate \$ A ^{-1} \$ directly. Since the sparsity structure of A- is not known, additional storage vectors are needed during the iteration. In the next section, an incomplete factorization \$ LU \$ of \$ A \$ is the starting point and we tried to improve this easy invertible approximation of \$ A \$. The update is constructed in such a way that the sparsity structure of \$ L \$ and \$ U \$ is maintained. Two different sparsity preserving updates are investigated from theoretical and practical point of view. Numerical experiments on discretized PDEs of convection diffusion type in 2- D with internal layers and on "arbitrary" matrices with symmetric sparsity structure are given. {\bf Key words:} nonsymmetric linear system, sparse secant method, Broyden's method, incomplete factorization.}, language = {en} } @misc{WulkowDeuflhard1990, author = {Wulkow, Michael and Deuflhard, Peter}, title = {Towards an Efficient Computational Treatment of Heterogeneous Polymer Reactions.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-292}, number = {SC-90-01}, year = {1990}, abstract = {The discrete Galerkin method developed by the authors has turned out to be an efficient tool for the computational treatment of very large scale ODE systems arising in polyreaction kinetics. Up to now, this approach has been worked out in detail for homogeneous polymer reactions. The present paper deals with one line of possible extensions of the method to the case of so-called heterogeneous processes, which may appear e. g. in smog reactions. The associated mathematical models involve reaction coefficients depending on the chain length of the reacting polymer. The herein suggested extension is worked out in some detail on the basis of the earlier paper. In addition, a numerical example describing polymer degradation is included.}, language = {en} } @misc{Giloi1990, author = {Giloi, Wolfgang K.}, title = {Konrad Zuses Plankalk{\"u}l als Vorl{\"a}ufer moderner Programmier-modelle. (Vortrag)}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4759}, number = {TR-90-13}, year = {1990}, language = {de} } @misc{NowakWeimann1990, author = {Nowak, Ulrich and Weimann, Lutz}, title = {GIANT - A Software Package for the Numerical Solution of Very Large Systems of Highly Nonlinear Equations.}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-4746}, number = {TR-90-11}, year = {1990}, abstract = {This report presents the final realization and implementation of a global inexact Newton method proposed by Deuflhard. In order to create a complete piece of software, a recently developed iterative solver (program GBIT) due to Deuflhard, Freund, Walter is adapted and serves as the standard iterative linear solver. Alternative linear iterative solvers may be adapted as well, e.g. the widely distributed code GMRES. The new software package GIANT (Global Inexact Affine Invariant Newton Techniques) allows an efficient and robust numerical solution of very large scale highly nonlinear systems. Due to the user friendly interface and its modular design, the software package is open for an easy adaptation to specific problems. Numerical experiments for some selected problems illustrate performance and usage of the package.}, language = {en} } @misc{CaprasseDemaretGatermannetal.1990, author = {Caprasse, H. and Demaret, J. and Gatermann, Karin and Melenk, Herbert}, title = {Power-Law Type Solutions of Fourth-Order Gravity}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-466}, number = {SC-90-18}, year = {1990}, abstract = {We study the power-law type solutions of the fourth order field equations derived from a generic quadratic Lagrangian density in the case of multidimensional Bianchi I cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the Groebner bases associated to it. While, in space dimension \$ d = 3 \$ , the Einsteinian Kasner metric is still the most general power-law type solution, for \$ d > 3 \$ , no solution, other than the Minkowski space-time, is common to the three systems of equations associated with the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the \$ d \$-dimensional space into a ( \$ d - 3 \$)-dimensional internal space and a physical 3- dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when \$ d = 9 \$).}, language = {en} }