MATH-250: Advanced numerical analysis I

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Lectures in this course (106)

Fixed Point Method: Convergence and Nonlinear Equations

Covers the fixed point method for solving nonlinear equations and discusses convergence properties.

Fixed Point Method: Global Convergence

Explores the fixed point method for global convergence in solving nonlinear equations.

Polynomial Interpolation: Optimizing Error

Covers the optimization of error in polynomial interpolation, focusing on minimizing the error by strategically placing interpolation points.

Iterative Methods: Linear Systems

Explores iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods, Cholesky factorization, and preconditioned conjugate gradient.

Absolute Stability in Digital Analysis

Explores absolute stability in digital analysis and Euler's methods through numerical schemes and verification processes.

Fixed Point Method: Proof

Explores the fixed point method for nonlinear equations and its convergence proof.

Polynomial Interpolation: Lagrange Method

Covers the Lagrange polynomial interpolation method and error analysis in function approximation.

Matrix Inversion: Pivoting and Iterative Methods

Explores matrix inversion, pivoting, and iterative methods for solving linear systems of equations.

Nonlinear Equations: Global Convergence of Fixed Point Method

Explores the global convergence of the fixed point method for nonlinear equations.

Absolute Stability of Euler Progressive Method

Explores the absolute stability of the Euler Progressive method and its significance in numerical solutions of differential equations.

Convergence Criteria: Richardson Method

Covers the Richardson method for solving linear systems and convergence criteria.

Stability of EP: Absolute Stability Property

Covers the concept of absolute stability property and stability conditions in EP.

Convergence Order

Explores the concepts of linear and quadratic convergence rates, highlighting their differences and applications in numerical methods.

Gradient Descent: Optimization Techniques

Covers optimization techniques related to gradient descent for finding the optimal solution iteratively.

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Absolute Stability in Numerical Methods

Explores absolute stability in numerical methods, emphasizing the control of disturbances in the solution.

Newton's Method: Convergence

Explores the convergence of Newton's method for solving nonlinear equations and the importance of selecting appropriate initial guesses.

Regression & Systemed Lineaires

Covers the principles of regression and linear systems, focusing on iterative methods.

Stability of Generalized Model Problem

Discusses the stability of a general model problem with a progressive Euler method.

Stability of Cauchy Problem: General Case Analysis

Explores stability conditions of the Cauchy problem in various scenarios.

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