30.17. Numerical Precision and Sensitivity

Try these first

1. 1.

   What is double precision arithmetic?

   Hint

   Think about how numbers are stored in a computer.

2. 2.

   Define numerical precision.

   Hint

   Refer to factors influencing computational accuracy.

3. 3.

   What problem is caused by floating-point roundoff errors?

   • A. Inaccurate calculations
   • B. Improved accuracy
   • C. Reduced computation time

   Hint

   Think about the challenges in computations.

4. 4.

   True or False: Double precision means increased accuracy due to more bits being used.

   • True
   • False

   Hint

   Recall the difference between double and single precision.

5. 5.

   Given a nearly singular matrix, describe how you would compute its eigenvectors while ensuring accuracy.

   Hint

   Consider what tools or software you might employ.

6. 6.

   In a simulation, you identify significant sensitivity in results due to rounding errors. Suggest a set of steps to improve the situation.

   Hint

   Address the problem iteratively.