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Subsection 6.1.3 What you will learn

  • 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.