Numerical Methods Final Exam 2023 Study Guide with
complete solution
All mathematical problems have a closed-form solution (i.e. they can be solved for a
variable without having to make guesses). (T/F)
False
___ can separate both array elements and multiple commands.
,(comma)
The false position algorithm is identical to the bisection algorithm, except for the
calculations for the estimated root location. (T/F)
true
The bisection method is a bracketing method. (T/F)
true
Bracketing methods always require two initial estimates. (T/F)
true
If an initial estimate is far from the root, open root-finding algorithms are more likely to
converge. (T/F)
False
The main advantage of the secant method is that it is guaranteed to converge. (T/F)
false
The parabolic interpolation method is based on fitting a parabola to two points on the
function.
false
One way to increase the accuracy of Newton-Cotes integration techniques is to
increase the number of segments.
true
The Trapezoidal Rule approximates the function by a first -order polynomial.
first
The composite Simpson's 3/8 Rule requires the number of segments to be [divisibility].
divisible by 3
The method of elimination involves eliminating unknowns by combining equations.
true
If one row of a matrix consists entirely of zeros, then the determinant is zero.
true
The determinant of a matrix is a scalar.
true
The determinant of ill-conditions systems is zero or nearly zero.
true
In the equation below, h is the step size.
yi+1=yi+(o)h
true
The midpoint method is usually more accurate than Euler's method for the same step
size.
true
complete solution
All mathematical problems have a closed-form solution (i.e. they can be solved for a
variable without having to make guesses). (T/F)
False
___ can separate both array elements and multiple commands.
,(comma)
The false position algorithm is identical to the bisection algorithm, except for the
calculations for the estimated root location. (T/F)
true
The bisection method is a bracketing method. (T/F)
true
Bracketing methods always require two initial estimates. (T/F)
true
If an initial estimate is far from the root, open root-finding algorithms are more likely to
converge. (T/F)
False
The main advantage of the secant method is that it is guaranteed to converge. (T/F)
false
The parabolic interpolation method is based on fitting a parabola to two points on the
function.
false
One way to increase the accuracy of Newton-Cotes integration techniques is to
increase the number of segments.
true
The Trapezoidal Rule approximates the function by a first -order polynomial.
first
The composite Simpson's 3/8 Rule requires the number of segments to be [divisibility].
divisible by 3
The method of elimination involves eliminating unknowns by combining equations.
true
If one row of a matrix consists entirely of zeros, then the determinant is zero.
true
The determinant of a matrix is a scalar.
true
The determinant of ill-conditions systems is zero or nearly zero.
true
In the equation below, h is the step size.
yi+1=yi+(o)h
true
The midpoint method is usually more accurate than Euler's method for the same step
size.
true
