Numerical Methods Final Exam Graded A+
All mathematical problems have a closed-form solution (i.e. they can be solved for
a variable without having to make guesses). (T/F) - ANS-False
___ can separate both array elements and multiple commands. - ANS-,(comma)
The false position algorithm is identical to the bisection algorithm, except for the
calculations for the estimated root location. (T/F) - ANS-true
The bisection method is a bracketing method. (T/F) - ANS-true
Bracketing methods always require two initial estimates. (T/F) - ANS-true
If an initial estimate is far from the root, open root-finding algorithms are more
likely to converge. (T/F) - ANS-False
The main advantage of the secant method is that it is guaranteed to converge.
(T/F) - ANS-false
The parabolic interpolation method is based on fitting a parabola to two points on
the function. - ANS-false
One way to increase the accuracy of Newton-Cotes integration techniques is to
increase the number of segments. - ANS-true
The Trapezoidal Rule approximates the function by a first -order polynomial. - ANS-
first
The composite Simpson's 3/8 Rule requires the number of segments to be
[divisibility]. - ANS-divisible by 3
The method of elimination involves eliminating unknowns by combining equations. -
ANS-true
If one row of a matrix consists entirely of zeros, then the determinant is zero. -
ANS-true
The determinant of a matrix is a scalar. - ANS-true
The determinant of ill-conditions systems is zero or nearly zero. - ANS-true
In the equation below, h is the step size.
All mathematical problems have a closed-form solution (i.e. they can be solved for
a variable without having to make guesses). (T/F) - ANS-False
___ can separate both array elements and multiple commands. - ANS-,(comma)
The false position algorithm is identical to the bisection algorithm, except for the
calculations for the estimated root location. (T/F) - ANS-true
The bisection method is a bracketing method. (T/F) - ANS-true
Bracketing methods always require two initial estimates. (T/F) - ANS-true
If an initial estimate is far from the root, open root-finding algorithms are more
likely to converge. (T/F) - ANS-False
The main advantage of the secant method is that it is guaranteed to converge.
(T/F) - ANS-false
The parabolic interpolation method is based on fitting a parabola to two points on
the function. - ANS-false
One way to increase the accuracy of Newton-Cotes integration techniques is to
increase the number of segments. - ANS-true
The Trapezoidal Rule approximates the function by a first -order polynomial. - ANS-
first
The composite Simpson's 3/8 Rule requires the number of segments to be
[divisibility]. - ANS-divisible by 3
The method of elimination involves eliminating unknowns by combining equations. -
ANS-true
If one row of a matrix consists entirely of zeros, then the determinant is zero. -
ANS-true
The determinant of a matrix is a scalar. - ANS-true
The determinant of ill-conditions systems is zero or nearly zero. - ANS-true
In the equation below, h is the step size.
