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CS3331: Numerical Methods
Quiz 2
April. 15, 1997
- 1.
- (4%)
- (a)
- What is the linear interpolation formula for a
function that passes two points
(a, f(a)) and (b, f(b))?
- (b)
- What is the error for the above
linear interpolation formula?
- 2.
- (6%) There are two ways to find an interpolation polynomial:
Lagrange interpolation and power series formulas.
What are the tow major advantages of using
the Lagrange interpolation formula over the other?
- 3.
- (2%) What is the MATLAB command for polynomial fitting?
- 4.
- (6%)
- (a)
- (4%)
What are the four shape functions
vi(x), ,
of the
Lagrange interpolation polynomial that passes
the following four points:
(1, y1), (2, y2), (3, y3), and (4, y4)?
(You don't need to expand the shape functions.)
- (b)
- (2%)
What is the Lagrange interpolation polynomial in
terms of the four shape functions?
- 5.
- (6%)
- (a)
- What is the general formula for the Chebyshev
polynomial?
- (b)
- What are the roots for the Chebyshev polynomial?
- (c)
- What is the advantage of using the roots as
the points for polynomial interpolation?
- 6.
- (6%)
A 2-input function passes the following four points:
i |
(xi, yi) |
zi |
1 |
(0, 0) |
1 |
2 |
(3, 0) |
4 |
3 |
(0, 2) |
3 |
4 |
(3, 2) |
6 |
Find the value at (1, 1) using the bilinear interpolation.
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J.-S. Roger Jang
3/20/1998