Numerical Computing: Stability and Error Analysis

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Related lectures (28)

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Nonlinear Equations: Methods and Applications

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Ill-posed Numerical Problems

Analyzes the impact of small errors in initial conditions on numerical solutions.

Numerical Methods: Iterative Techniques

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Fixed Point Theorem: Convergence of Newton's Method

Covers the fixed point theorem and the convergence of Newton's method, emphasizing the importance of function choice and derivative behavior for successful iteration.

System of ODEs

Explores numerical methods for solving ODE systems, stability regions, and absolute stability importance.

Stochastic Differential Equations: Mean-Field Inference

Explores inference for stochastic differential equations, focusing on numerical methods and convergence analysis.

Composite Formulas Analysis

Discusses the analysis of composite numerical integration formulas and their convergence, stability, and error characteristics.

Root Finding Methods: Secant, Newton, and Fixed Point Iteration

Covers numerical methods for finding roots, including secant, Newton, and fixed point iteration techniques.