Term
| What does it mean for a problem to be well-conditioned? |
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Definition
| Perturbations to the input data cause relatively small changes in the solution |
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Term
| Formalize conditioning of a problem |
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Definition
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If the condition number of f(x) is small, then the problem is well-conditioned |
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Term
| When would 1-D function evaluation be poorly conditioned? |
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Definition
| When the function has a large slope |
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Term
| When would it be a good idea to use a relative condition number instead of an absolute condition number? |
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Definition
| You always want to use relative cond unless either the input or solution values are expected to be zero (root finding problem) |
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Term
| What is a problem that is inherently ill conditioned? |
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Definition
| Differentiation -- small change in function can cause drastic change to the value of the derivative |
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Term
| What does backward error mean? |
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Definition
| The amount of change to the input values that would explain all of the error in the solution |
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Term
| Consider a linear system Ax = b and suppose we perturb the right hand side b, which in turn perturbs the solution x. Can you derive the conditioning of this problem? |
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Definition
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