Office : Room # 417, Bharti Building

Email : amitk@cse.iitd.ac.in

Phone : (ext) 1286.

1. Homework 1 (due Jan 19, 2018)

2. Homework 2 (due Feb 2, 2018)

3. Homework 3 (due March 12, 2018)

4. Homework 4 (due April 1, 2018)

5. Homework 5 (due April 16, 2018)

6. Homework 6 (due May 4, 2018)

Lecture 2: Condition number, floating point operations ( [H] Chapter 1, [TB] Chapter 12)

Lecture 3: Stability, review of linear algebra ([H] Chapter 1, [TB] Chapter 14, Chapter 15, Chapter 1)

Lecture 4: Review of linear algebra

Lecture 5: Linear transformations, norms of matrices ([TB] Chapter 3)

Lecture 6: Singular value decomposition, properties of matrices using SVD ([TB] Chapter 4, Chapter 5)

Lecture 7: Proof of SVD Theorem, low rank approximation. (TB Chapter 4, Chapter 5)

Lecture 8: Applications of SVD. Condition Number of a matrix. (TB Chapter 5, Chapter 12)

Lecture 9: Latent Semantic Indexing

Lecture 10: QR factorization, QR using Gram Schmidt. ([TB] Chapter 7,8)

Lecture 11: Householder transformation, QR factorization via Householder. ([TB] Chapter 10)

Lecture 12: Stability of QR factorization. Least Squares Problem. ([TB] Chapter 16, Chapter 11)

Lecture 13: Conditioning of Least Squares Problem and solution using QR factorization. ([TB] Chapter 18, 19)

Lecture 14: Guassian Elimination and LU factorization ([TB] Chapter 20)

Lecture 15: LUP factorization and stability of Gaussian Elimination ([TB] Chapter 21, 22)

Lecture 16: Positive semidefinite matrices and Cholesky factorization ([TB} Chapter 23)

Lecture 17: Eigenvalues: existence, diagonalizability, applications to ODE ([TB] Chapter 24, [H] Example 9.7)

Lecture 18: Schur factorization, eigenvalues of symmetric matrices, Reduction to Hessenberg form ([TB] Chapter 25, 26)

Lecture 19: Power iteration, convergence, Rayleigh quotient ([TB] Chapter 27)

Lecture 20: Pagerank Algorithm

Lecture 21: Inverse iteration, Rayleigh iteration and cubic convergence ([TB] Chapter 27)

Lecture 22: Simultaneous iteration and convergence, conditioning of eigenvalue problems ([H] Chapter 4.3, 4.5.5)

Lecture 23: Convex functions and unconstrained optimization ([H] Chapter 6.2, [BV] Chapter 3)

Lecture 24: More on convexity, Gradient Descent ([H] Chapter 6.3, [BV] Chapter 9.3)

Lecture 25: Smoothness, strong convexity, analysis of gradient descent for smooth and strongly convex functions ([BV] Chapter 9.3)

Lecture 26: Preconditioning in gradient descent, Newton's method and various ways to derive Newton's method, affine invariance([BV] Chapter 9.5)

Lecture 27: Optimization with equality and inequality constraints, duality, KKT conditions ([BV] Chapter 5.1, 5.5)

Lecture 28: Examples of KKT conditions ([BV] Chapter 5.5)

Lecture 29: Newton's method with equality constraints, some basic ideas of barrier methods for inequality constraints ([BV] Chapter 10.2.1)

Lecture 30: IVP for Ordinary Differential Equations, concept of stable solutions, accuracy (Heath Chapter 9.1, 9.2)

Lecture 31: Euler's method, Implicit Euler's method, trapezoid method, solving an equation using fixed point iteration (Heath Chapter 9.3, 5.5.2)

Lecture 32: More on solving systems of equations using Newton's method and its variants (Heath Chapter 5.5.3, 5.5.4)

Lecture 33: Taylor series methods, problems with Taylor series methods, accuracy of Taylor's method (Heath Chapter 9.3.5)

Lecture 34: Runge Kutta method, derivation of 2nd order and 3rd order methods (Heath Chapter 9.3.6)

Lecture 35: Multi-step methods, derivation of multi-step methods using interpolation (Heath Chapter 9.3.8)

You will be expected to write programs in MATLAB.

1. [CK] Numerical Mathematics and Computing, by Ward Cheney and David Kincaid.

2. [H] Scientific Computing : an introductory survey, by Michael T. Heath.

3. [TB] Numerical Linear Algebra, by Llyod N. Trefethen and David Bau.

4. [BV] Convex Optimization , by Boyd and Vanderberghe.

20% : Each minor exam

35% : Major exam