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 $x i = b i$ 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