## Course Detail

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

### Syllabus

##### 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.

### References

‘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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