Parallel Matrix Computations

This page is last updated on February 28, 2026.

Assignment-2

Pre-requisites: 

MA-II (MA002), Programming

Course Syllabus: 

[Unit-1] Introduction: Computing determinants, trace, inverse, adjoint, transpose and their computational cost; Various types of matrices and their properties. Elementary and permutation matrices, elementary transformation, row echelon, and reduced row echelon forms. Rank, properties of rank, applications of rank. Matrix Norms, inner products, condition number.     

[Unit-2] Fundamentals of Parallel Computations: Introduction to High performance and parallel computing; Its requirement; Forms of parallelism, parallel architecture, types of operations; Addition and multiplication of matrices using parallel algorithms; parallel environment in MATLAB and basic syntax. Block decomposition of matrices and performance analysis in parallel environment. Parallel solver of system of linear equations. 

Course Outcomes: 

The present course will provide a computational perspective of parallel matrix computations. By attending the course, students will be able to understand 

1. Various matrix computations and associated computational cost.

2. Requirement of parallel computing and various sources.

3. Parallel computations related to addition, multiplication, and block decomposition.

4. Parallel computations in MATLAB.       

Recommended Books:

Text Books:

1. Matrix Computations, 4th edition by G. Golub and C. Van Loan. John Hopkins, 2015.

2. Numerical linear algebra by Lloyd N. Trefethen and David Bau, III. SIAM, 1997.

3. Iterative methods for sparse linear systems (2nd edition) by Yousef Saad

4. Direct methods for sparse linear systems by T. A. Davis, SIAM publishing, 2006.

Reference Books:

1. Introduction to Parallel Computing, 2nd edition, by V. Kumar, A. Grama, A. Gupta, and G. Karypis (2003).  

2. Georg Hager and Gerhard Wellein, Introduction to High-Performance Computing for Scientists and Engineers, Chapman&Hall/CRC, Special Indian Edition, 2011.

Evaluation Scheme: 

Students will be evaluated on a scale of 100 = {Assg1, Ass2, Exam} where

Assg1,2 - Assignment - 30 Marks each for 1 Hr duration

Exam - Open Book Exam - 40 Marks for 1.5 Hr duration 

Note: A minimum of 20 out of 100 marks is required to pass the course. The grading will be relative-scaled.

Exam/Test Schedule: 

1. Assignment -1 will held on 19th January 2026. 

2. Assignment -2 will held on 16th February 2026.

3. Open book exam will held during the time of mid-term exams.