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MA213: Numerical Analysis
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MCQs on Numerical Analysis.

MA213: Numerical Analysis
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25 Questions

1. The term Initial Value Problem is best defined in this course as which of the following?
2. If
is the Lagrange interpolator for the knots
and
, what is
?
3. Which of the following is an implicit method?
4. If an IVP is stiff, what restriction is imposed on the solver?
5. Fill in the blank. If a small change to a problem leads to a large change in its solution, then we say that the problem is ______________.
6. What is the truncation error term for the 3-point centered difference formula for approximating
?
7. Suppose it is known that the continuous function
has exactly 1 root strictly between 0 and 1, and it is not a double root. Which method can guarantee an approximate root with error less than 0.0001 in fewer than 14 function evaluations?
8. Problem
has input
and output
. A small perturbation
gives a new input
and a new output
. A relative condition number
for problem
should satisfy which of the following?
9. Which of the following is true for
?
10. What type of polynomial interpolator would be appropriate for the data
?
11. Which of the following is a Newton iteration to find
?
12. Let
be the value of the
derivative of a curve at the point
. Suppose we want to interpolate the data
and
. If a Vandermonde matrix is constructed for the interpolating polynomial, what is its size?
13. What is the Taylor polynomial of degree 1 for
at
?
14. Choose the iteration below which represents the Runge-Kutta method called the modified Euler or Heun's method.
15. What is an upper bound on the relative error between two neighboring floats called?
16. A shooting method for a boundary value problem requires what 2 numerical methods?
17. Which of the following is true for
?
18. The Weierstrauss approximation theorem says that under certain conditions on
and for any
, there is a polynomial
, such that
for all
. Choose from below the weakest such conditions on
?
19. Use a 3-point centered difference formula with
to approximate
, where

. Identify the best 4 significant digit approximate below.
20. Consider the Lagrange basis functions for the knots
, and
. How many basis functions are there for this set of knots, and what are their degrees?
21. How many polynomials exist which interpolate the data
where
for
?
22. Fill in the blank. A second order ordinary differential equation,
requires two extra conditions for uniqueness of solution. If these conditions are
and
, then the differential equation is called a(n) ___________.
23. Suppose it is known that the continuous function
has exactly 1 root strictly between 0 and 1, and it is a double root. An encrypted subroutine will return
given any
. Which of the following methods cannot be applied to this problem?
24. Which of the following is a Newton iteration to find
?
25. When dividing a polynomial
of degree
by the polynomial
, the remainder will be a scalar. What choice below best describes this scalar?

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