Term
What does it mean for a problem to be wellconditioned? 

Definition
Perturbations to the input data cause relatively small changes in the solution 


Term
Formalize conditioning of a problem 

Definition
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If the condition number of f(x) is small, then the problem is wellconditioned 


Term
When would 1D 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

