Unit 6.1.3 What you will learn
This week, you explore how roundoff error when employing floating point computation affect correctness.
Upon completion of this week, you should be able to
Recognize how floating point numbers are stored.
Employ strategies for avoiding unnecessary overflow and underflow that can occur in intermediate computations.
Compute the machine epsilon (also called the unit roundoff) for a given floating point representation.
Quantify errors in storing real numbers as floating point numbers and bound the incurred relative error in terms of the machine epsilon.
Analyze error incurred in floating point computation using the Standard Computation Model (SCM) and the Alternative Computation Model (ACM) to determine their forward and backward results.
Distinguish between conditioning of a problem and stability of an algorithm.
Derive error results for simple linear algebra computations.
State and interpret error results for solving linear systems.
Argue how backward error can affect the relative error in the solution of a linear system.