Deck 14: Numerical Methods

Question 1

Typically, ____ equations involve trigonometric, exponential, or logarithmic functions and cannot be reduced to any polynomial equation in x .

A) quadratic
B) transcendental
C) real
D) linear

Answer 1

B

Question 2

In the ____ method, you can predict with some precision the number of iterations required to find a function s root to a certain accuracy.

A) interpolation
B) derivative
C) bisection
D) regula falsi

Answer 2

C

Question 3

A root-finding method that uses a minimum of finesse is known as a ____ method.

A) light
B) hypothetical
C) fine
D) brute-force

Answer 3

D

Question 4

Many of the theorems you learned for roots of polynomials don t apply to transcendental equations.

Question 5

The regula falsi procedure can be made to converge more rapidly if the interval can be made to collapse from only one direction.

Question 6

A polynomial of degree n has precisely ____ roots.

A) n-1
B) n
C) n+2
D) 2*n

Question 7

Using the ____ root-finding method, the interval is made to collapse from both directions.

A) modified regula falsi
B) regula falsi
C) bisection
D) integration

Question 8

The ____ method presents the basics on which most root-finding methods are constructed.

A) bisection
B) binary
C) guessing
D) interval

Question 9

With the regula falsi method of root-finding, success is based on the size of the function, not the size of the interval.

Question 10

The real roots of polynomials are usually classified as being either ____ numbers or irrational.

A) royal
B) integer
C) rational
D) transcendental

Question 11

An approximation to the area under a complicated curve is obtained by assuming the function can be replaced by simpler functions over a limited range.

Question 12

Simpson s rule converges nicely in most instances and it is easy to use.

Question 13

The regula falsi root-finding method is essentially the same as bisection, except instead of using the interval s midpoint at each step of the calculation, you use a(n) ____ value for the root.

A) modified
B) endpoint
C) integrated
D) interpolated

Question 14

The secant method of root-finding does not pose divergence problems.

Question 15

By using information about the ____ of a functional value in addition to its sign, you can speed up the convergence of your root-finding scheme.

A) type
B) size
C) phase
D) rationality

Question 16

One of the most common tasks in science and engineering is finding the roots of equations.

Question 17

Numerical integration is a stable process.

Question 18

A change in a function s ____, indicating the vicinity of a root has been located, forms the key element in the computer code for locating roots.

A) name
B) parameters
C) sign
D) data type

Question 19

A straight line is the simplest approximation to a function.

Question 20

Simpson s rule is a popular method of evaluating integrals of functions that are smooth.

Question 21

Among the bisection, regula falsi, and modified regula falsi methods, the ____ method is probably the most efficient for common problems.

A) bisection
B) regula falsi
C) modified regula falsi
D) all of the above are equally efficient

Question 22

____ rule is based on approximating a function by straight-line segments.

A) The trapezoidal
B) Simpson s
C) Bart s
D) Dijkstra s

Question 23

____ consists of expressing the area as the sum of areas of smaller segments.

A) The derivative
B) Rooting
C) Numerical differentiation
D) Numerical integration

Question 24

A(n) ____ is a number used to alter the results of one iteration before inserting them into the next.

A) iteration factor
B) relaxation factor
C) increment
D) booster

Question 25

In the ordinary ____________________ method, the only feature of the function that is monitored is its sign.

Question 26

The ____ method is probably the most popular method for finding the root of a function.

A) secant
B) bisection
C) interpolation
D) interval

Question 27

Irrational numbers and transcendental numbers are represented by ____________________ decimal fractions and cannot be expressed as simple fractions.

Question 28

The ____ root-finding method uses a predictable number of iterations.

A) modified regula falsi
B) trigo-sine
C) inverted parabola
D) bisection

Question 29

The ____ of a function of a single variable can be thought of as the area under a curve.

A) derivative
B) integration
C) name
D) root

Question 30

____ rule is based on approximating a function by parabolic segments.

A) The trapezoidal
B) Simpson s
C) Bart s
D) Dijkstra s

Question 31

The ____ method is identical to the regula falsi method, except the sign of f ( x ) doesn t need to be checked at each iteration.

A) brute-force
B) secant
C) regula falsi
D) modified regula falsi

Question 32

A drawback of the ____________________ method is that even though the method converges more rapidly to a value of x that results in a small |f(x)| , the interval containing the root does not diminish significantly.

Question 33

In numerical integration, excessive computation times typically occur when the number of iterations exceeds ____.

A) 5
B) 10
C) 25
D) 50

Question 34

Numerical integration is fairly safe from problems such as ____.

A) round-off errors
B) division by zero
C) convergence
D) both a and b

Question 35

An approximation to the area under a complicated curve is obtained by assuming the function can be replaced by simpler functions over a limited ____.

A) range
B) time
C) phase
D) matrix

Question 36

Specifying a parabola uniquely requires ____ points.

A) three
B) four
C) five
D) six

Question 37

The art of ____________________ analysis consists in balancing time spent optimizing a problem s solution before computation against time spent correcting unforeseen errors during computation.

Question 38

The lowest-order Simpson s rule has ____ panel(s).

A) no
B) one
C) two
D) three

Question 39

The chapter text cautions that the secant root-finding method can pose ____ problems.

A) convergence
B) rounding
C) computer memory
D) divergence

Question 40

The regula falsi method will almost always ____________________faster than the conventional bisection method.

Question 41

To increase the accuracy of numerical integration methods, the interval is simply subdivided into a larger number of ____________________.

Question 42

Many, perhaps most, of the integrals occurring in actual engineering or science problems cannot be expressed in any ____________________ form.

Question 43

Determining the optimum ____________________ (slope-reduction) factor is almost always an extremely difficult problem in any calculation.

Question 44

The area under a curve can be approximated by connecting a line between two points on the curve and calculating the area under that line. The shape created is called a(n) ____________________.

Question 45

In numerical integration, excessive ____________________ times is a potential problem.

Question 46

The number of ____________________ is not predictable in the regula falsi and modified regula falsi methods.

Question 47

____________________ error occurs when the values of f ( x 1) and f ( x 3) used in the computation are nearly equal.

Question 48

Of the three bisection methods, the ___________________ is probably the most efficient for common problems.

Question 49

The ____________________ method can be shown to be equivalent to replacing the function repeatedly by straight lines drawn through the points x 0 , f ( x 0 ) and x 1 , f ( x 1 ) .

Question 50

The very simplest approximation to a function is a(n) ____________________.