Lecture 5 of 40Week 1
Iterative methods-II
Prof. Ameeya Kumar Nayak and Prof. Sanjeev Kumar · IIT Roorkee
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- Numerical methods, IIT Roorkee (at NPTEL)
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- CC BY-NC-SA, as NPTEL states it. Non-commercial use only.
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All the lectures
- Introduction to error analysis and linear systems
- Gaussian elimination with partial pivoting
- LU decomposition
- Jacobi and Gauss Seidel methods
- Iterative methods-II
- Introduction to Non-linear equations and Bisection method
- Regula Falsi and Secant methods
- Newton-Raphson method
- Fixed point iteration method
- System of Nonlinear equations
- Introduction to Eigenvalues and Eigenvectors
- Similarity Transformations and Gershgorin Theorem
- Jacobi's Method for Computing Eigenvalues
- Power Method
- Inverse Power Method
- Interpolation Part I (Introduction to Interpolation)
- Interpolation part-II ( Some basic operators and their properties)
- Interpolation part-III (Newton’s Forward/ Backward difference and derivation of general error)
- Interpolation part-IV (Error in approximating a function by a polynomial using Newton’s Forward & Backward difference formula)
- Interpolation part-V (Solving problems using Newton's Forward & Backward difference formula)
- Interpolation part-VI (Central difference formula)
- Interpolation part-VII (Lagrange interpolation formula with examples)
- Interpolation part-VIII (Divided difference interpolation with examples)
- Interpolation part-IX (Hermite's interpolation with examples)
- Numerical differentiation part-I (Introduction to numerical differentiation by interpolation formula)
- Numerical differentiation part-II (Numerical differentiation based on Lagrange’s interpolation with examples)
- Numerical differentiation part-III (Numerical differentiation based on Divided difference formula with examples)
- Numerical differentiation part-IV (Maxima and minima of a tabulated function and differentiation errors)
- Numerical differentiation part-V (Differentiation based on finite difference operators)
- Numerical differentiation part-VI (Method of undetermined coefficients & Derivatives with unequal intervals)
- Numerical Integration part-I (Methodology of Numerical Integration & Rectangular rule )
- Numerical Integration part-II (Quadrature formula and Trapezoidal rule with associated errors)
- Numerical Integration part-III (Simpsons 1/3rd rule with associated errors)
- Numerical Integration part-IV (Composite Simpsons 1/3rd rule & Simpsons 3/8th rule with examples)
- Numerical Integration part-V (Gauss Legendre 2-point and 3-point formula with examples)
- Introduction to Ordinary Differential equations
- Numerical methods for ODE-1
- Numerical Methods-II
- R-K Methods for solving ODEs
- Multi-step Method for solving ODEs