Numerics topics

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For the exam, you should:

  • Be able to express a given problem as a set of linear equations and/or a set of least-squares constraints
  • Be able to eliminate constraints of the form xi = bi from a set of constraints.
  • Understand how to solve linear equations and least-squares when the coefficient matrix is upper triangular with no zeros on the diagonal.
  • Understand the mechanics of a Givens rotation (which elements of A and b are replaced by what linear combinations).
  • Understand how a sequence of Givens rotations can zero all the elements of a system below the main diagonal, leaving the matrix upper triangular.

You DO NOT need to be able to:

  • Derive the equations for a Givens rotation.
  • Understand how to treat singular problems (e.g., a triangular A but with zeros on the diagonal).
  • Know anything about numerical stability issues
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