Numerical Methods Exam 1

Question 1

A NASA intern is writing a function with a single input in MATLAB to help detect sunspots automatically, but unfortunately they never payed attention in numerical methods and can’t remember how.

function sunspots(telescopeData)

Answer 1

(telescopeData)

Question 2

The equation below is being evaluated in MATLAB. For each labeled operation, indicate whether it requires a dot operator.
a0 and gc are scalars, and V9, m0 and M0 are vectors of the same length.
T = a0 m0 / gc (V9 / a0 - M0)

Answer 2

a) The multiplication between a0 and m0.
No

b) The divide between m0 and gc.
Yes

c) The multiplication between gc and term in ().
Yes

d) The division between V9 and a0.
No

e) The subtraction between a0 and M0.
No

Question 3

The order of the truncation error is reduced as more terms of the infinite series are included in the calculation.

Answer 3

True

Question 4

The golden section method helps to minimize computational costs in finding a maximum/minimum

Answer 4

True

Question 5

The secant method is similar to the Newton-Raphson method, but it does not require the derivative of the function to be known

Answer 5

it does not require the derivative of the function to be known

Question 6

Only disadvantage of the Newton-Raphson method is that it requires the user to analytically find the derivative of the function

Answer 6

True

Question 7

The secant method is similar to the ___ method(s)

Answer 7

Newton-Raphson
False Position

Question 8

A bracket with opposite-signed function values always contains exactly one root.

Answer 8

False

Question 9

Bracketing methods are based on the idea that if two function values f1 and f2 have ______, there must be at least one root between them

Answer 9

opposite signs

Question 10

The main disadvantage of the false position method is that it is one-sided

Answer 10

True

Question 11

A numerical method is a well-defined procedure to solve a problem

Answer 11

True

Question 12

the equal sign, ‘=’, is used to assign data to a variable

Answer 12

True

Question 13

Anonymous functions need to be defined before being used

Answer 13

True

Question 14

Truncation Error occur when using finite terms to represent an infinite series

Answer 14

True

Question 15

Which name is valid for a variable

Answer 15

GPA no skipping invalid

3_skipped_labs_GPA invalid

GPA-3-skipped-labs invalid

GPA_no_skipping valid

Question 16

There are many causes of Round-off error. What is one of those causes?

Answer 16

The computer is limited in how precisely we can store numbers

Question 17

discontinuous functions can result in a bracket with opposite-signed function values having an even number of roots

Answer 17

True

Question 18

The bisection method is most effective when there are multiple roots inside a bracket. (T/F)

Answer 18

False

Question 19

The main disadvantage of the false position method is that it can diverge. (T/F)

Answer 19

False

Question 20

Newton-Raphson is not an iterative method. (T/F)

Answer 20

False

Question 21

The secant method requires two initial estimates of x, but does not require an analytical expression of the derivative. (T/F)

Answer 21

True

Question 22

MATLAB’s built-in fzero function is uses a combination of bisection, secant, and inverse quadratic interpolation methods and a search method if only one input is provided . (T/F)

Answer 22

True

Question 23

Select all of the root-finding methods that require only one initial guess. Check all that apply:

Answer 23

Newton- Raphson
Modified Secant

Question 24

The golden section method divides the interval into three sections.

Answer 24

True

Question 25

Numerical methods can be used to solve problems with open form solutions.

Answer 25

True

Question 26

Pseudocode is ________.

Answer 26

a computer-like implementation of a flowchart that does not use any particular program’s syntax

Question 27

MATLAB’s fminsearch function can be used to find the minimum value of a function of two or more independent variables

Answer 27

True

Question 28

All mathamatical problems have a closed - form solution (they can be solved for a variable without having to make guesses.

Answer 28

false

Question 29

A computer scientist is attempting to automate the process of cooking hamburgers . They are using MATLAB to analyze some data, and need a function file that doesn’t have any output variables. Click the dropdown menu to complete the header.
function flippingBurgers(burgerTemperature,juiceIndex,condimentArray)

Answer 29

function

Question 30

What is the closest correct definition of Round-off error?

Answer 30

An error that arises because of how many digits of a number are used.

Question 31

The main advantage of the bisection algorithm is that it always converges

Answer 31

True

Question 32

Tangent points in a function can cause an opposite valued bracket to contain an even number of roots (T/F)

Answer 32

True

Question 33

The secant method is similar to the newton-raphson method, but it uses an approximation of the derivative (T/F)

Answer 33

True

Question 34

In the golden section method, if f(x1) < f(x2), then the new search interval is from xlow to x1.

Answer 34

False