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Allgower E.L., Georg K. Introduction to numerical continuation methods

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Allgower E.L., Georg K. Introduction to numerical continuation methods
Colorado State University, 1990. — 397 p.
Over the past ten to fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. These two methods have been called by various names. One of the methods has been called the predictor-corrector or pseudo arc-length continuation method. This method has its historical roots in the imbedding and incremental loading methods which have been successfully used for several decades by engineers and scientists to improve convergence properties when an adequate starting value for an iterative method is not available. The second method is often referred to as the simplicial or piecewise linear method. This method has its historical roots in the Lemke-Howson algorithm for solving nonlinear complementarity problems. The idea of complementary pivoting has been adapted and applied to the calculation of fixed points of continuous maps and of semi-continuous set valued maps. In this book we endeavor to provide an easy access for scientific workers and students to the numerical aspects of both of these methods.
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