Numerical Linear Algebra

Start Date
22/01/2018

End Date
13/04/2018

No. of
Enrollments
61 students

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Created by

Agrawal P. N
IIT Roorkee
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Course Language
English
Course Type
Scheduled
Video transcripts
English
Course Category
Engineering
Learning Path
Undergraduate
Course Length
30 Hours
Weekly time commitments
20 Hours
Course Completion
Yes, after passing all tests. View Certificate
Exam Date
To be announced
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Weekly Reading list

Overview

For certification please click here

 

Last date for enrollment: January 22, 2018

ABOUT THE COURSE

This course is a basic course offered to UG/PG students of Engineering/Science background. It contains basics of matrix algebra, computer arithmetic, conditioning and condition number, stability of numerical algorithms, vector and matrix norms, convergent matrices, stability of non-linear systems, sensitivity analysis, singular value decomposition (SVD), algebraic and geometric properties of SVD, least square solutions, Householder matrices and applications, QR method, Power method and applications, Jacobi method for finding the eigenvalues of a given matrix. This course has tremendous applications in diverse fields of Engineering and Sciences such as control theory, image processing, numerical analysis and dynamical systems etc.



INTENDED AUDIENCE
UG and PG students of technical institutions/ universities/colleges


PRE-REQUISITES
None


INDUSTRY SUPPORT – LIST OF COMPANIES/INDUSTRY THAT WILL RECOGNIZE/VALUE THIS ONLINE COURSE
None

To access the content, please enroll in the course.

Faculty

Agrawal P. N


Dr. P. N. Agrawal is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes approximation Theory and Complex Analysis. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Further he has completed online certification course “Mathematical methods and its applications” jointly with Dr. S.K. Gupta of the same department. He taught the course on “Integral equations and calculus of variations” several times to MSc (Industrial Mathematics and Informatics) students. He has supervised nine Ph.D. theses and has published more than 187 research papers in reputed international journals of the world. 

Dr.  D. N Pandey is an Associate Professor in the Department of Mathematics, IIT Roorkee. Before joining IIT Roorkee he worked as a faculty member in BITS-Pilani Goa campus and LNMIIT Jaipur. His area of expertise includes semigroup theory, functional differential equations of fractional and integral orders. He has already prepared e-notes for course titled “Ordinary Differential Equations and Special Functions” under e-Pathshala funded by UGC. Also, he has published a book titled “Nonlocal Functional Evolution Equations: Integral and fractional orders, LAP LAMBERT Academic Publishing AG Germany”. He has delivered several invited talks at reputed institutions in India and abroad. He has guided three Ph.D. theses and has published more than 75 papers in various international journals of repute. Currently, he is supervising five research students. 

COURSE LAYOUT

Week 1: Matrix operations and type of matrices, Determinant of a Matrix, Rank of a matrix, Vector Space-I, Vector Space-II

Week 2:
Linear dependence and independence, Bases and Dimensions – I, Bases and Dimension - II, Linear Transformation - I, Linear Transformation - II

Week 3: Orthogonal subspaces, Row space, column space and null Space, Eigenvalues and Eigenvectors-I, Eigenvalues and Eigenvectors-II, Diagonalizable Matrices

Week 4: Orthogonal Sets, Gram Schmidt orthogonalization and orthonormal bases, Introduction to Matlab, Sign integer representationComputer representation of numbers

Week 5: Floating point representation, Round-off error, Error propagation in computer arithmetic, Addition and multiplication of floating point numbers, Conditioning and condition numbers-I

Week 6: Conditioning and condition numbers-II, Stability of numerical algorithms-I, Stability of numerical algorithms-II, Vector norms - I, Vector norms - II

Week 7: Matrix  Norms - I, Matrix Norms-II, Convergent Matrices - I, Convergent Matrices - II, Stability of non-linear system

Week 8: Condition number of a matrix: Elementary properties, Sensitivity analysis-I, Sensitivity analysis-II, Residual theorem, Nearness to singularity

Week 9: Estimation of the condition number,  Singular value decomposition of a matrix – I, Singular value decomposition of a matrix - II, Orthogonal Projections, Algebraic and geometric properties of  matrices using SVD

Week 10: SVD and their applications, Perturbation theorem for singular values, Outer product expansion of a matrix, Least square solutions-I, Least square solutions-II

Week 11: Psudeo - inverse  and least square solution, Householder  matrices  and their applications, Householder QR factorization –I, Householder QR factorization –II, Basic theorems on eigenvalues and QR method

Week 12: Power method, Rate of convergence of  Power method, Applications of Power method with shift, Jacobi method-I, Jacobi method-II

 
SUGGESTED READING

1. V. Sundarapandian, Numerical Linear Algebra, PHI, 2008.
2. Biswa Nath Dutta, Numerical Linear Algebra and Applications, SIAM, 2010. 
3. Roger A. Horn and Charles R. Johnson, Matrix Analysis, Cambridge University Press, 1994. 
4. William Ford, Numerical Linear Algebra with Applications, Academic Press, 2014..

 
 

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