Numerical Linear Algebra, August-December 2018

Credits 9 credits
When F slot (Tuesday,Wednesday, Thursday, Friday)
Where Humanities and Sciences Block, Room 266


Sivaram Ambikasaran,
Office hours: 2PM-4PM, Mondays, HSB 241C

Teaching Assistant

Vaishnavi Gujjula,
Office hours: 2PM-4PM, Wednesdays

Flyer The course flyer can be found here

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Lecture Summary


First Class will be on August 1, 2018, Wednesday. Below is a tentative calendar, which will be updated as we make progress in the course.
Week Tuesday Wednesday Thursday Friday Assignment
Jul 30- Aug 3 No class Motivation Chapter 1; BD Chapter 1; BD Assign-1: Due Aug 8 Drop Assignment; Solution
Aug 6-10 Chapter 1,2; BD Holiday Chapter 2; BD No class Assign-2: Due Aug 15 Drop Assignment; Solution
Aug 13-17 No class Class on Monday; Chapter 3, BD Chapter 3, BD Gaussian elimination and the need for pivoting Assign-3: Due Aug 22 Drop Assignment; Solution
Aug 20-24 No Class Holiday Stability LU factorization Assign-4: Due Aug 29 Drop Assignment; Solution
Aug 27-31 No Class LU factorization and asymptotically optimal algorithms Partial Pivoted LU Quiz-I, August \(31\) Quiz-I solutions; Performance summary Assign-5: Due Sept 5 Drop Assignment; Solution
Sep 3-7 No class No class No class Complete pivoting, cost of pivoting, Cholesky Assign-6: Due Sept 12 Drop Assignment; Solution
Sep 10-14 No class Cholesky, Least squares Holiday No class Assign-7: Due Sept 26 Drop Assignment; Solution
Sep 17-21 Least squares, Least norm (Monday) Holiday Assign-8: Due Sept 30 Drop Assignment; Solution
Sep 24-28
Oct 1-5 Assign-9: Due October 21 Drop Assignment
Oct 8-12 Quiz-II, October \(12\), Quiz-II solutions
Oct 15-19 Holiday
Oct 22-26
Oct 29-Nov 2
Nov 5-9 Last day of class Assign-10: Due November 14Drop Assignment
Nov 26-30 EndSem, November \(27\)


Evaluation Assignments Quiz-I Quiz-II Final Exam
Points 30 15 15 40

Detailed Syllabus

Matrix and vector norms, floating points arithmetic, forward and backward stability of algorithms, conditioning of a problem, perturbation analysis, algorithmic complexity, Solving linear systems, Gaussian elimination, LU factorization, Pivoting, Cholesky decomposition, Iterative refinement, QR factorization, Gram-Schmidt orthogonalization, Projections, Householder reflectors, Givens rotation, Singular Value Decomposition, Least squares and least norm solution of linear systems, pseudoinverse, normal equations, Eigenvalue problems, Gershgorin theorem, Similarity transform, Eigenvalue & eigenvector computations and sensitivity, Power method, Schur decomposition, Jordan canonical form, QR iteration with & without shifts, Hessenberg transformation, Rayleigh quotient, Symmetric eigenvalue problem, Jacobi method, Divide and Conquer, Computing the Singular Value Decomposition, Golub-Kahan-Reinsch algorithm, Chan SVD algorithm, Rank and matrix approximations, image compression using SVD, Generalized SVD, Generalized and Quadratic eigenvalue problems, generalized Schur decomposition (QZ decomposition), Iterative methods for large linear systems: Jacobi, Gauss-Seidel and SOR, convergence of iterative algorithms, Krylov subspace methods: Lanczos, Arnoldi, MINRES, GMRES, Conjugate Gradient and QMR, Pre-conditioners, Approximating eigenvalues and eigenvectors, Structured matrix computations, Designing matrix algorithms on modern computer architectures


We will be drawing material from all three books. Notes will be posted as and when required.

Other useful texts to read:

Other references


Practice Final-I Practice Final-II
Exam Date
Quiz-I August \(31\), Friday
Quiz-II October \(12\), Friday
End Term November \(27\), Tuesday