NUMERICAL METHODS TRUE/FALSE

True percent relative error is a measure of precision.

False (measure of accuracy)

An nth order polynomial has n real or complex roots.

True

The truncation error for a 3rd order Taylor series is O(h^4).

True

Polynomial deflation is the process of removing roots from transcendental functions.

False

If a numerical method has an error O(h^2), where h is the step size [xi+1=xi], halving the step size will quarter the error.

True

In general, using more bits to store a number will reduce round-off error.

True

A computers finite storage space is a source of truncation errors.

False (round-off error)

If a numerical method provides an approximate with error O(h), where h is the step size, doubling the step size will halve the error.

False

The bracket interval [Xu-Xl] is reduced by the same percentage for each iteration of the bisection method.

True

Precision refers to how closely approximations agree with each other.

True

The machine epsilon describes the worst-case scenario truncation error.

False

The interval between numbers that can be represented with fixed-point-notation increases as magnitude increases.

False

The round-off error caused by storing numbers with floating point representation is not consistent and varies greatly with the magnitude of the number being stored.

False

If a numerical method provides an approximate error O(h^2), where h is the step size, doubling the step size will quarter the error.

False

The error resulting from a Taylor series approximation will decrease as the step size h decreases.

True

The False Position Method takes into account the magnitude of the function at the guesses (Xi and Xu).

True

The Secant Method is similar to the Newton Raphson Method, but it uses an approximation for the derivative.

True

When open methods converge, they do so faster than bracket methods.

True

It is ok to use the approximate percent relative error for numerical methods because the approximate percent relative error will always be less than the true percent relative error.

False

If the magnitude of the condition number is larger than 1 (>>1), the system is considered well-conditioned.

False

True percent relative error is a measure of accuracy.

True

Storing only a few digits of pi is a source of truncation error.

False

The floating point storage scheme allows computers to store most numbers exactly.

False

Open methods for finding roots are slow but reliable when compared to bracket methods.

False

The standard error of the estimate describes the spread of the data around the mean value.

False

A unique nth order polynomial fit requires n-1 data points.

False

A regression line has merit if the standard error of the estimate is smaller than the standard deviation.

True

If the regression line passes directly through all data points, then the coefficient of determination will be equal to one.

True

Consider a linear system of equations in Matrix Form (Ax=B).

The solution is: x=BA^-1, where A^-1 is the inverse of the A matrix.

False

Consider a linear system of equations in Matrix Form (Ax=B).

The linear system is considered well conditioned if the determinant of A equals zero.

False

Consider a linear system of equations in Matrix Form (Ax=B).

The Gauss-Seidel method will always converge on the solution, (assuming one exist)

False

Consider a linear system of equations in Matrix Form (Ax=B).

It is more efficient to use LU decomposition to solve for A^-1 than Gauss elimination.

True

Consider a linear system of equations in Matrix Form (Ax=B).

The system can be solved (assuming a solution exist) by: x=A^-1B, where A^-1 is the inverse of matrix A.

True

Consider a linear system of equations in Matrix Form (Ax=B).

If the determinant of the matrix A equals zero, partial pivoting is necessary to solve the system.

False

Consider a linear system of equations in Matrix Form (Ax=B).

Assuming a solution exist, solving using LU decomposition will be more efficient than Naive Gauss Elimination.

False

Consider a linear system of equations in Matrix Form (Ax=B).

The system is considered ill-conditioned if the condition number equals 500.

True

Consider a linear system of equations in Matrix Form (Ax=B).

Scaling the equations by 10 (i.e. multiplying both sides of the equations by 10) will affect the determinant as well as the solution.

False

Gauss-Jordan elimination is a more efficient variation of Gauss elimination.

False

If a matrix is multiplied by its inverse, the result will be the identity matrix.

True

If AY=I, where I is the identity matrix, Y must equal A^-1.

True

The norm of a matrix is a measure of its length.

True

LU decomposition is more efficient than Gauss elimination when solving for the inverse of a matrix.

True

The gradient of a function f(x,y) only indicates the direction of steepest ascent.

False

For a two dimensional function f(x,y), the point where (df/dx)=(df/dy)=0 always indicates an optima.

False

The random search scheme always finds a global extremum.

True

Partial pivoting can help avoid division by zero when used with Gauss elimination.

True

Parabolic interpolation approximates the optima location using a 3rd order polynomial fit.

False

Consider a function f(x,y). The x,y location where both df/dx=0 and df/dy=0 will not always be an optima.

True