MAE 284 Final exam 2022 with complete solution The parabolic interpolation method is based on fitting a parabola to three points on the function.Answer - True The golden section method helps to minimize computational costs in finding a maximum/minimum.Answer - True The key benefit to the golden section method is that we do not have to calculate both x1 and x2 at each iteration.Answer - True The parabolic interpolation method is usually faster than the golden section method.Answer - True Adaptive Quadrature adjusts to use a smaller step size in areas where the function changes rapidly, and a larger step size where the function changes slowly.Answer - True Romberg's method is a Newton-Cotes method.Answer - True The error for the "normal" accuracy versions of the forward, backward, and centered finite difference approximations is O(h).Answer - False Numerical differentiation is not particularly susceptible to errors in data.Answer - False Simpson's 1/3 Rule approximates the function by a ______ -order polynomial.Answer - Second Romberg's method is NOT a Newton-Cotes method.Answer - False The only way to increase the accuracy of a numerical approximation of a derivative is to add more terms in the Taylor Series used to derive the approximation.Answer - False The error for the "normal" accuracy versions of the forward, backward, and centered finite difference approximations is O(h2).Answer - False The determinant of a matrix is a scalar.Answer - True If two rows of a matrix are interchanged, the determinant changes sign.Answer - True
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