Newtonian Methods in Nonlinear Problems (Informatics)
Type: For the student's choice
Department: computational mathematics
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In this course there are being studied: iterative-difference and iterative-parametric methods, methods for solving nonlinear operator equations, nonlinear least squares problems and unconstrained minimization problems, methods with the approximation of the inverse operators and methods with using internal linear iterations for solving nonlinear systems of equations. The global strategies for quasi-Newton iterative methods, linear algorithms for large systems, nonlinear algorithms focused on decreasing residual and error, inexact Newton methods and global methods of Gauss-Newton type for nonlinear least squares problems are being considered. Much attention is paid to the theoretical aspects of the methods, studying the convergence of methods, advanced modern algorithms and their implementation on computers.