## Unit6.1.3What 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.