Computer Algorithms and Modelling
Q1.
An important computation used in Statistics for the normal distribution is the following
P=0.5+12πx=ax=bex22dx
Write a JAVA program using a simple menu based system to assist you in your investigation of three numerical integration techniques: rectangular rule, trapezoidal rule and Simpson’s rule for computing ND given above.
Analysis of results: This should include a well documented and clearly presented table for the case when a=0, b=1 and show the results using 4, 64, 128, 512 and 1024 strips, obtained by using the three numerical rules given above.
(3 methods x 2 marks per strip case x 5 strip cases = 3 x 2 x 5 = 30 marks.)
Conclusions: Discuss what you consider to be the most accurate method, the most efficient method and also what is the approximation to P.
Report all your answers to 5 decimal places).
Deliverables:
Deliverable 1 – the report in PDF format should contain:
User documentation guide of how to use the program
Analysis of results (see above for detailed breakdown of what is required)
Conclusions (see above for detailed breakdown of what is required)
Deliverable 2 – the well commented JAVA source code
The correctly functioning Java source code uploaded as a zip file
Q2.
// use fori loop to process rows
for (i = 0, i < n; i++) {
// use forj loop to process columns
for (j = 0; j < n; j++) {
// solutions are stored into array c
c[i][j] = s * a[i][j] + b[i][j];
}
}
Determine the computational count in terms of n for the code above and include the loop header cost in the count.
operation 
Time taken (microseconds) 
add 
1 
subtract 
1 
multiply 
2 
divide 
3 
assign 
0.5 
compare 
0.5 
Using these timings calculate the time taken to execute the code in 2(a) when n=5, 500, 50000, 500000 and 5000000. You should show all working out in each calculation as well as providing the completed table below. Your answers should be in the time unit of seconds:
n 
Time taken to execute code in (a) above (seconds) 
5 

500 

50000 

500000 

5000000 
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