Details of MA5110 (Autumn 2013)

Level: 5 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA5110 Numerical Linear Algebra Priyanka Shukla

Syllabus
Basics: Basics Matrix-vector Multiplication, Orthogonal Vectors and Matrices, Norms, Singular Value Decomposition, Projection, QR Factorization, Gram-Schmidt Orthogonalization, Householder Triangularization, Least Squares Problems.
Conditioning and Stability: Conditioning and Condition Numbers, Floating Point Arithmetic,
Stability: Stability of Householder Triangularization, Stability of Back Substitution, Stability of Least Squares Algorithms.
Systems of Equations: Gaussian Elimination, Pivoting, Stability of Gaussian Elimination, Cholesky Factorization.
Eigenvalues: Eigenvalue Problems, Overview of Eigenvalue Algorithms, Reduction to Hessenberg or Tridiagonal Form, Rayleigh Quotient,Inverse Iteration.
Iterative Methods: Overview of Iterative Methods, Arnoldi Iteration, GMRES, Lanczos Iteration, Conjugate Gradients, Preconditioning

References
L. N. Trefethen and D. Bau (1997) Numerical Linear Algebra, SIAM. (Main Text Book)
Y. Saad (1991) Numerical Methods for Large Eigenvalue Problems, Manchester University Press.
Y. Saad (2003) Iterative Methods for Sparse Linear Systems, SIAM.
G. H. Golub and C. F. Van-Loan (1983) Matrix computations, Johns Hopkins University Press.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Elective
2 IP 3 Elective
3 MS 9 Elective
4 RS 1 Elective