Unsw Maths2089 June 2011 Exam Paper

FAMILY NAME: . . . . . . . . . . . . . . . . . . . . . . . . . . . . OTHER NAME(S):. . . . . . . . . . . . . . . . . . . . . . . . . . STUDENT NUMBER: . . . . . . . . . . . . . . . . . . . . . . SIGNATURE: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

THE UNIVERSITY OF NEW SOUTH WALES SCHOOL OF MATHEMATICS AND STATISTICS

June 2011

MATH2089 Numerical Methods and Statistics

(1) TIME ALLOWED – 3 Hours (2) TOTAL NUMBER OF QUESTIONS – 6 (3) ANSWER ALL QUESTIONS (4) THE QUESTIONS ARE OF EQUAL VALUE (5) THIS PAPER MAY NOT BE RETAINED BY THE CANDIDATE (6) ONLY CALCULATORS WITH AN AFFIXED “UNSW APPROVED” STICKER MAY BE USED (7) STATISTICAL FORMULAE ARE ATTACHED AT END OF PAPER STATISTICAL TABLES ARE ATTACHED AT END OF PAPER

Part A – Numerical Methods consists of questions 1 – 3 Part B – Statistics consists of questions 4 – 6 Both parts must be answered

All answers must be written in ink. Except where they are expressly required pencils may only be used for drawing, sketching or graphical work.

June 2011

MATH2089

Page 2

Part A – Numerical Methods
1.

Answer in a separate book marked Question 1
a) What are the values produced by the following Matlab expressions: i) x = -1e+200; ans1 = log(exp(x)) ii) v = [-1:1] ans2 = v./v.^(1/2) iii) x = 200; h = 1e-14; ans3 = x + h > x b) The computational complexity of some common operations with n by n matrices are Operation Matrix multiplication LU factorization Cholesky factorization Back/forward substitution Tridiagonal solve Flops 2n3
2n3 + O(n2 ) 3 n3 + O(n2 ) 3 2

n + O(n) 8n + O(1)

i) Estimate the size of the largest symmetric positive definite linear system that can be solved in one hour on a 2.5 GHz 6-core computer, where each core can do two floating point operations per clock cycle. ii) A symmetric n by n matrix is determined by the n(n+1) elements Ai,j 2 for j = 1, . . . , n, i = 1, . . . , j. Estimate the size of the largest n by n symmetric matrix that can be stored in a