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MA50178: Numerical linear algebra

Follow this link for further information on academic years Academic Year: 2018/9
Further information on owning departmentsOwning Department/School: Department of Mathematical Sciences
Further information on credits Credits: 6      [equivalent to 12 CATS credits]
Further information on notional study hours Notional Study Hours: 120
Further information on unit levels Level: Masters UG & PG (FHEQ level 7)
Further information on teaching periods Period:
Semester 1
Further information on unit assessment Assessment Summary: CW 40%, EX 60%
Further information on unit assessment Assessment Detail:
  • Coursework (CW 20%)
  • Class Test (CW 20%)
  • Examination (EX 60%)
Further information on supplementary assessment Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Further information on requisites Requisites:
Further information on descriptions Description: Aims:
To teach an understanding of iterative methods for standard problems of linear algebra.

Learning Outcomes:
Students should know a range of modern iterative methods for solving linear systems, the algebraic eigenvalue problem and least squares problems. They should be able to analyse their algorithms and should have an understanding of relevant practical issues.

Problem Solving (T,F&A), Computing (T,F&A), independent study and report writing.

Topics will be chosen from the following:
Linear matrix eigenvalue problem: The Schur form. The power method and its extensions. Subspace methods. Error analysis and convergence theory. Perturbation theory. Givens/Householder QR factorization and the QR method. The Lanczos method and extensions. Krylov subspace methods. The Jacobi algorithm. The Divide and Conquer method. Extensions to generalised and nonlinear eigenvalue problems. Special matrix classes and applications. The Singular Value Decomposition and applications.
Iterative methods for linear systems: Convergence of stationary iteration methods. Descent methods and the conjugate gradient method and extensions. Krylov subspace methods and preconditioners. Relationship between Lanczos and conjugate gradient method. Error bounds and perturbation theory. Convergence and extensions. Special matrix classes and applications.
Least squares problems: Full-rank and rank-deficient least squares problems, Normal equations, QR decompostion, Singular value decompostion, low-rank approximation and applications.
Further information on programme availabilityProgramme availability:

MA50178 is Optional on the following programmes:

Department of Mathematical Sciences