Introduction to Numerical Continuation Methods
Numerical continuation methods have provided important contributions toward the numerical solution of nonlinear systems of equations for many years. The methods may be used not only to compute solutions, which might otherwise be hard to obtain, but also to gain insight into qualitative properties of the solutions. Introduction to Numerical Continuation Methods, originally published in 1979, was the first book to provide easy access to the numerical aspects of predictor corrector continuation and piecewise linear continuation methods. Not only do these seemingly distinct methods share many common features and general principles, they can be numerically implemented in similar ways. Introduction to Numerical Continuation Methods also features the piecewise linear approximation of implicitly defined surfaces, the algorithms of which are frequently used in computer graphics, mesh generation, and the evaluation of surface integrals.
Autres éditions - Tout afficher
affine Allgower arclength barycenter bifurcation point boundary calculate chapter clface co-ordinates completely labeled N-face computational cond conjugate gradient method continuation methods convergence convex corrector step defined denote dimension discussion double precision eigenvalue endif error estimate facet finite fixed point formula function given Givens rotation global goto Hence homotopy method implementation initial value problem integer inverse iteration Jacobian lambda lemma map H matrix meshsize Newton steps Newton's method nonlinear norm f nplusk numerical numerically stable obtain orthogonal output parameter Peitgen period perturbation pivoting step PL algorithm PL approximation PL manifold PL methods PL steps point of H polynomial predictor step predictor-corrector proof QR decomposition regular value return end subroutine Rheinboldt simple bifurcation point slist smooth map solution curve solving starting simplex steplength adaptation stepsize subroutine sufficiently small tangent theorem transverse traversing triangulation update variable vector vertex zero point