Reichel W. Numerical methods for Electrical Engineering, Meteorology,...2022 torrent

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Direct methods
Introduction
Gaussian elimination and the LR-decomposition
The Cholesky decomposition
The QR-decomposition (supplement)
Eigenvalue problems
Concepts and de nitions
The von-Mises iteration
The inverse iteration of Wielandt
The LR-method and the QR-method for eigenvalue problems (Supplement)
Householder's method of reduction to Hessenberg resp tridiagonal matrix shape (Supplement)
Linear Programming (or Linear Optimization)
Error analysis
Introduction
Propagation of errors in systems of linear equations
Newton method
Numerical quadrature
Introduction
The trapezoidal rule and the rectangle rule
Quadrature formulas based on interpolation
Newton-Côtes formula
Numerical solutions of initial value problems
Introduction
Introduction to the solution theory of initial value problems
Euler's method
One-step methods - De nitions and elementary properties
The method of Taylor comparison
Runge-Kutta-methods of consistency order
General Runge-Kutta methods
Convergence of one-step methods and an error estimate
Final remarks
Finite di erences for boundary value problems
Discretization for boundary value problems for ordinary di erential equations
Discretization of boundary value problems for partial di erential equations
Finite Elements
Weak formulations of boundary value problems
Ritz-Galerkin approximation
Implementation of the Ritz-Galerkin method