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Course Detail

Course Name Computer Solutions of Linear Algebraic Systems
Course Code 18CS736
Credits Coimbatore
Year Taught 2018


Course Syllabus

Matrix Multiplication Problems: Structure and Efficiency, Block Matrix and Algorithms, Fast Matrix vector products. Matrix Analysis: Vector Spaces, Norms, Matrix norms, Orthogonality, Singular value Decomposition, Sensitivity of Square systems, Finite precision matrix computation. Linear Systems: Triangular Systems, LU Factorization, Parallel LU, Diagonal Dominance and Symmetry, Positive Definite Systems, Banded Systems. Orthogonalizations and Least squares: Householder and Givens Transformation, QR Factorization.

Parallel Matrix Computation: Basic concepts, Cost of Communication, Challenge of Load Balancing, Tradeoffs, Shared Memory Systems, Parallel Matrix Multiplication. Eigen value Computation: Power Iteration, Jacobi Method.

Course Outcome

At the end of the course the students will be able to:

Course Outcome Bloom’s Taxonomy Level
CO 1 Analyze the efficiency of matrix multiplication in terms of data access, storage and flops L4
CO 2 Understand and implement the iterative methods for eigen value computation L2
CO 3 Compute/Evaluate the efficiency of matrix factorizations in finding solutions to linear systems, matrix transformations: LU factorization, Positive definiteness, QR factorization L5
CO 4 Analyze the sensitivity of square systems, finite precision computations L4
CO 5 Understand the basic concepts in parallel matrix computation L2
CO 6 Apply the concepts of parallel programming and implement parallel matrix computations L3

Text Books / References

  1. Golub and Loan, “Matrix Computations”, John Hopkins University Press, Fourth Edition.
  2. Carl. D. Meyer, “Matrix Analysis and Applied Linear Algebra”, SIAM., 2000.


‘Computer Solutions of Linear Algebraic Systems’ is an elective course offered in M. Tech. in Computer Science and Engineering program at School of Engineering, Amrita Vishwa Vidyapeetham.

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