Numerics topics
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(Difference between revisions)
(New page: 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...) |
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For the exam, you should: | 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 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. | + | * Be able to eliminate constraints of the form <math>x_i=b_i</math> 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 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 the mechanics of a Givens rotation (which elements of <math>A</math> and <math>b</math> 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. | * 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: | You DO NOT need to be able to: | ||
* Derive the equations for a Givens rotation. | * Derive the equations for a Givens rotation. | ||
| - | * Understand how to treat singular problems (e.g., a triangular A but with zeros on the diagonal). | + | * Understand how to treat singular problems (e.g., a triangular <math>A</math> but with zeros on the diagonal). |
* Know anything about numerical stability issues | * Know anything about numerical stability issues | ||
Latest revision as of 22:37, 13 December 2008
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
