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ex5 - CS70 Discrete Mathematics for Computer Science Spring...

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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 degree-3 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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