CS70 Discrete Mathematics for Computer Science, Spring 2012
Homework 5
Out: 16 Feb. Due: 5pm, 23 Feb.
Instructions:
Start each problem on a new sheet. Write your name,
section number
and “CS70” on every sheet.
If you use more than one sheet for a problem, staple them together (but do
not
staple different problems together).
Put your solutions in the boxes on Soda level 2 by 5pm on Thursday: your solution to Q1 goes in box CS70–1, your
solution to Q2 goes in box CS70–2, and so on (
five
boxes total). You are encouraged to form small groups (two to four
people) to work through the homework, but you
must
write up all your solutions on your own.
1. [Polynomial interpolation]
Consider the set of four points
{
(0
,
1)
,
(1
,

2)
,
(3
,
4)
,
(4
,
0)
}
.
(a) Construct the unique degree3 polynomial (over the reals) that passes through these four points by
writing down and solving a system of linear equations.
(b) Repeat part (a) but using the method of Lagrange interpolation. Show your working clearly, and use
the same notation as in Lecture Note 7.
2. [Representing polynomials]
Let
f
be a polynomial of degree at most
d
. The
coefficient representation
of
f
is the sequence
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 Spring '08
 PAPADIMITROU
 Computer Science, PointValue Representation

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