# Shared Flashcard Set

## Details

Matthew Qual Questions
Matthew's Qual Questions
8
Computer Science
03/07/2014

Term
 What does it mean for a problem to be well-conditioned?
Definition
 Perturbations to the input data cause relatively small changes in the solution
Term
 Formalize conditioning of a problem
Definition
 [image] If the condition number of f(x) is small, then the problem is well-conditioned
Term
 When would 1-D function evaluation be poorly conditioned?
Definition
 When the function has a large slope
Term
 When would it be a good idea to use a relative condition number instead of an absolute condition number?
Definition
 You always want to use relative cond unless either the input or solution values are expected to be zero (root finding problem)
Term
 What is a problem that is inherently ill conditioned?
Definition
 Differentiation -- small change in function can cause drastic change to the value of the derivative
Term
 What does backward error mean?
Definition
 The amount of change to the input values that would explain all of the error in the solution
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?
Definition
 [image][image]
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