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MAE 284 EXAM Q&A 2026 STUDY GUIDE PRACTICE SOLUTION, Exams of Design and Analysis of Algorithms

Princeton UniversityDesign and Analysis of Algorithms

MAE 284 EXAM Q&A 2026 STUDY GUIDE PRACTICE SOLUTION

Typology: Exams

2025/2026

Available from 12/23/2025

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MAE 284 EXAM Q&A 2026 STUDY GUIDE
PRACTICE SOLUTION
⫸ Eigenvalues are the solutions of the the equation |A-ambdaI| = 0
Answer: True
⫸ What technique did we use to solve nonlinear finite-difference
equations?
Gauss-Seidel
Linear Interpolation
Something else Answer: Gauss_Seidel
⫸ For linear ODEs, linear interpolation can be used with the shooting
method to guarantee the correct solution on the third "shot" Answer:
True
⫸ There are three "types" of numerical derivative approximations:
forward, backward, and centered Answer: True
⫸ The error for the lower accuracy versions of the forward, backward
and centered finite difference approximations is O(h^2) Answer: False
⫸ In general, a numerical solution is an exact solution Answer: False
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MAE 284 EXAM Q&A 2026 STUDY GUIDE

PRACTICE SOLUTION

⫸ Eigenvalues are the solutions of the the equation |A-ambdaI| = 0 Answer: True ⫸ What technique did we use to solve nonlinear finite-difference equations? Gauss-Seidel Linear Interpolation Something else Answer: Gauss_Seidel ⫸ For linear ODEs, linear interpolation can be used with the shooting method to guarantee the correct solution on the third "shot" Answer: True ⫸ There are three "types" of numerical derivative approximations: forward, backward, and centered Answer: True ⫸ The error for the lower accuracy versions of the forward, backward and centered finite difference approximations is O(h^2) Answer: False ⫸ In general, a numerical solution is an exact solution Answer: False

⫸ Pseudocode is- Answer: A computer-like description of steps that does not use any particular computer language's syntax or grammar ⫸ A student is attempting to create a function file named quiz1_question4.m. After three tries, they type a function declaration that works correctly. All four attempts are listed below. Which one of the listed function declarations is error-free? quiz1_question4(a,b,c) = [d,e] function [d,e] = quiz1_question4(a,b,c) quiz1_question4(a,b,c) = function [d,e] function [d,e] = boss_function(a,b,c) Answer: function [d,e] = quiz1_question4(a,b,c) ⫸ What is round-off error? Answer: An error that arises because of how many digits of a number are used ⫸ Tangent points in a function can cause an opposite-valued bracket to contain an even number of roots Answer: True ⫸