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Rabinowitz Ph. Numerical methods for nonlinear algebraic equation

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Rabinowitz Ph. Numerical methods for nonlinear algebraic equation
London, New York, Paris - 1970. - 209 p.
Editor Rabinowitz Ph.
Книга посвящена численным методам решения нелинейных алгебраических уравнений и их систем.
A review of methods for solving nonlinear algebraic equations in one variable.
Introduction.
Iterative methods which require no evaluation of derivatives.
Methods which depend on both the function and its derivative.
Computational efficiency.
Methods suitable for difficult problems.
The determination of an algorithm which uses the mixed strategy technique for the solution of single nonlinear equations.
Introduction.
Iteration functions.
Efficiency of iteration functions.
Selection of iteration functions.
General description of algorithm.
Design of computer program.
Computational experience.
Concluding remarks.
Appendix.
A numerical method for locating the zeros and poles of a meromorphic function.
Introduction.
Theoretical considerations.
Tests for the rank of the matrices G(m).
Proposed algorithms.
Numerical examples.
Discussion.
Recent developments in solving nonlinear algebraic systems.
Introduction.
Methods using the explicit Jacobian.
Methods for approximating the Jacobian.
Matrix updating procedures.
Davidenko's method.
Recent developments.
Generalized inverses for nonlinear equations and optimization.
Introduction.
Nonlinear equations.
Optimization.
A hybrid method for nonlinear equations.
Introduction.
A cautionary example.
The new algorithm, given first derivatives.
Numerical approximations to derivatives.
Discussion.
A fortran subroutine for solving systems of nonlinear algebraic equations.
Introduction.
The parameters of the subroutine.
An outline of the algorithm.
The calculation of δ.
The revision of ∆.
The revision of J.
Maintaining linear independence.
Other details of the algorithm.
Numerical examples.
Conclusion.
On the convergence of newton-like methods.
Preliminaries.
Results.
A finite difference.
Newton method.
Concluding remarks.
Matrix iteration and acceleration processes in finite element problems of structural mechanics.
Introduction.
The finite element process in linear elasticity.
Nonlinearities due to material properties only.
Nonlinearities due to large deformation.
Acceleration of convergence.
Multiple roots.
References.
A short bibliography on solution of systems of nonlinear algebraic equations.
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