numerical analysis mid test

Select the best definition for “numerical analysis”:

• the study of round-off errors

• the study of algorithms for computing approximate solutions to problems from continuous mathematics

• the study of quantitative approximations to the solutions of mathematical problems including consideration of and bounds for the errors involved

• the branch of mathematics that deals with the development and use of numerical methods for solving

  problems

How many significant digits does the floating point number 0.03140 × 103 have?

• 6

• 5

• 4

• 3

Suppose that a hypothetical binary computer stores floating point numbers in 16-bit words as shown. What is machine epsilon for this computer?

• 2 ⁻¹⁶

• 2 ^-12

• 2 ^-8

• 2 ^-4

Let ˆx be some approximation of x. Which of the following error definitions is correct?

• 
• 
• 
• 

If f(x) is a real-valued function of a real variable, then the error in the

difference approximation for the derivative

• absolute

• relative

• cancellation

• truncation

In floating-point arithmetic, which of the following operations on two positive floating-point numbers can produce an overflow?

• addition and subtraction

• multiplication and division

• All

• None

Let f(x) = x 2 − 2x + 1. The bisection method can be used to approximate the root of the function f(x) pictured.

• True

• False

The ___________of a measurement is given by the difference between

the approximate value and its underlying true value.

• Input error

• Truncation error

• relative error

• absolute error

The of a measurement is given by the absolute error divided

by the true value.

• Input error

• relative error

• Absolute error

6.43200 has ___ significant digits

• 7

• 5

• 6

• 4