Question

1. What is the Maclaurin series for the function sin(x)? Please determine the minimum number of terms needed to compute sin(0.1) accurate to 12 decimal places (rounded), using a) Taylor’s theorem and b) alternating series theorem.

Show your work and justify your answers for the above problem.

2. Create two random matrices A and B each of size ? × ?. Write a computer program in Java or Matlab to compute

a) D(i, j) = A(i, j) * B(i, j) for i = 1 … n and j = 1 … n, and

b) D(i, j) = ∑ (A(i,k) ∗ B(k,j)) ? ?=1 for i= 1 … n and j = 1 … n.

Use a timing function to report the execution time for the two computations using single and then double precisions. Report on the execution time of each run. Try n = 100 and 1000.

c) repeat the calculations in (a) and (b) above using Matlab.

1. What is the Maclaurin series for the function sin(x)? Please determine the minimum number of terms needed to compute sin(0.1) accurate to 12 decimal places (rounded), using a) Taylor's theorem and b) alternating series theorem. Show your work and justify your answers for the above problem. 2. Create two random matrices A and B each of size n x n. Write a computer program to compute a) D(i, j) = A(i, j) * B(i, j) for i=1 ... n and j=1 ... n, and b) Di, j) = XR-1(Ai, k) * B(k,j)) for i=1 ... n and j = 1 ... n. Use a timing function to report the execution time for the two computations using single and then double precisions. Report on the execution time of each run. Try n= 100 and 1000. c) repeat the calculations in (a) and (b) above using Matlab.

Answer 1

2)

clc%clears screen
clear all%clears history
close all%closes all files
format long
n=10;
A=rand(n);
B=rand(n);
D=[];
tic;
for i=1:n
for j=1:n
D(i,j)=A(i,j)*B(i,j);
end
end
t1=toc;
D=[];
tic;
for i=1:n
for j=1:n
D(i,j)=0;
for k=1:n
D(i,j)=D(i,j)+A(i,k)*B(k,j);
end
end
end
t2=toc;
disp('part a time for double');
disp(t1)
disp('part b time for double');
disp(t2)
A=single(rand(n));
B=single(rand(n));
D=[];
tic;
for i=1:n
for j=1:n
D(i,j)=A(i,j)*B(i,j);
end
end
t1=toc;
D=[];
tic;
for i=1:n
for j=1:n
D(i,j)=single(0);
for k=1:n
D(i,j)=D(i,j)+A(i,k)*B(k,j);
end
end
end
t2=toc;
disp('part a time for single');
disp(t1)
disp('part b time for single');
disp(t2)