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Lecture 34 of 49Advanced Numerical Analysis

Lecture 34 : Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.)

Prof. Sachin C. Patwardhan · IIT Bombay

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Advanced Numerical Analysis, IIT Bombay (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

  1. Lecture 1: Introduction and Overview Video
  2. Lecture -2 Fundamentals of Vector Spaces Video
  3. Lecture 3 : Basic Dimension and Sub-space of a Vector Space Video
  4. Lecture 4 : Introduction to Normed Vector Spaces Video
  5. Lecture 5 : Examples of Norms,Cauchy Sequence and Convergence, Introduction to Banach Spaces Video
  6. Lecture 6 : Introduction to Inner Product Spaces Video
  7. Lecture 7 : Cauchy Schwaz Inequality and Orthogonal Sets Video
  8. Lecture 8 : Gram-Schmidt Process and Generation of Orthogonal Sets Video
  9. Lecture 9 : Problem Discretization Using Appropriation Theory Video
  10. Lecture 10 : Weierstrass Theorem and Polynomial Approximation Video
  11. Lecture 11 : Taylor Series Approximation and Newton's Method Video
  12. Lecture 12 : Solving ODE - BVPs Using Firute Difference Method Video
  13. Lecture 13 :Solving ODE - BVPs and PDEs Using Finite Difference Method Video
  14. Lecture 14 : Finite Difference Method (contd.) and Polynomial Interpolations Video
  15. Lecture 15 : Polynomial and Function Interpolations,Orthogonal Collocations Method for Solving ODE -BVPs Video
  16. Lecture 16 : Orthogonal Collocations Method for Solving ODE - BVPs and PDEs Video
  17. Lecture 17 :Least Square Approximations, Necessary and Sufficient Conditions for Unconstrained Optimization Video
  18. Lecture 18 : Least Square Approximations :Necessary and Sufficient Conditions for Unconstrained Optimization Least Square Approximations ( contd..) Video
  19. Lecture 19 :Linear Least Square Estimation and Geometric Interpretation of the Least Square Solution Video
  20. Lecture 20 : Geometric Interpretation of the Least Square Solution (Contd.) and Projection Theorem in a Hilbert Spaces Video
  21. Lecture 21 : Projection Theorem in a Hilbert Spaces (Contd.) and Approximation Using Orthogonal Basis Video
  22. Lecture 22 :Discretization of ODE-BVP using Least Square Approximation Video
  23. Lecture 23 : Discretization of ODE-BVP using Least Square Approximation and Gelarkin Method Video
  24. Lecture 24 : Model Parameter Estimation using Gauss-Newton Method Video
  25. Lecture 25 : Solving Linear Algebraic Equations and Methods of Sparse Linear Systems Video
  26. Lecture 26 : Methods of Sparse Linear Systems (Contd.) and Iterative Methods for Solving Linear Algebraic Equations Video
  27. Lecture 27 : Iterative Methods for Solving Linear Algebraic Equations Video
  28. Lecture 28 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Eigenvalues Video
  29. Lecture 29 :Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms Video
  30. Lecture 30 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis using Matrix Norms (Contd.) Video
  31. Lecture 31 : Iterative Methods for Solving Linear Algebraic Equations: Convergence Analysis (Contd.) Video
  32. Lecture 32 :Optimization Based Methods for Solving Linear Algebraic Equations: Gradient Method Video
  33. Lecture 33 : Conjugate Gradient Method, Matrix Conditioning and Solutions of Linear Algebraic Equations Video
  34. Lecture 34 : Matrix Conditioning and Solutions and Linear Algebraic Equations (Contd.) Video
  35. Lecture 35 : Matrix Conditioning (Contd.) and Solving Nonlinear Algebraic Equations Video
  36. Lecture 36 : Solving Nonlinear Algebraic Equations: Wegstein Method and Variants of Newton's Method Video
  37. Lecture 37 : Solving Nonlinear Algebraic Equations: Optimization Based Methods Video
  38. Lecture 38 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis of Iterative Solution Techniques Video
  39. Lecture 39 : Solving Nonlinear Algebraic Equations: Introduction to Convergence analysis (Contd.) and Solving ODE-IVPs Video
  40. Lecture 40 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Basic Concepts Video
  41. Lecture 41 :Solving Ordinary Differential Equations - Initial Value Problems (ODE-IVPs) : Runge Kutta Methods Video
  42. Lecture 42 :Solving ODE-IVPs : Runge Kutta Methods (contd.) and Multi-step Methods Video
  43. Lecture 43 :Solving ODE-IVPs : Generalized Formulation of Multi-step Methods Video
  44. Lecture 44 : Solving ODE-IVPs : Multi-step Methods (contd.) and Orthogonal Collocations Method Video
  45. Lecture 45 : Solving ODE-IVPs: Selection of Integration Interval and Convergence Analysis of Solution Schemes Video
  46. Lecture 46 : Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) Video
  47. Lecture 47 :Solving ODE-IVPs: Convergence Analysis of Solution Schemes (contd.) and Solving ODE-BVP using Single Shooting Method Video
  48. Lecture 48 : Methods for Solving System of Differential Algebraic Equations Video
  49. Lecture 49 : Methods for Solving System of Differential Algebraic Equations (contd.) and Concluding Remarks Video