Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

3 Question for Computational Methods and Software - Assignment 2 | CS 417, Assignments of Computer Science

Old Dominion UniversityComputer Science

Material Type: Assignment; Class: Computational Methods and Software; Subject: Computer Science; University: Old Dominion University; Term: Unknown 1989;

Typology: Assignments

Pre 2010

Uploaded on 02/12/2009

koofers-user-ins
koofers-user-ins 🇺🇸

9 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
CS 417/517 Computational Methods and Software
Spring 2004
HW 2
Assigned: Thurs Jan 29, 2004; Due: Thurs Feb 5, 2004
Homework problems will be posted in the course directory:
www.cs.odu.edu/˜pothen/Courses/CS417. If any corrections are found to be neces-
sary, they will be posted in this directory as well. You must show your work to receive credit for
your answers. In problems where you are asked to give reasons, an answer without a stated reason
will receive no credit.
1. Answer the following questions as true or false, giving a reason for your answer.
(a) Floating point addition is commutative: the order in which two numbers are written
when they are added makes no difference to the result; i.e., a+b=b+a.
(b) Floating point addition is associative: the order in which three numbers are added,
makes no difference to the result; i.e., (a+b) + c=a+ (b+c).
(c) If two real numbers can be exactly represented as floating point numbers, then their
exact sum can always be represented as a floating point number without any rounding
errors.
(d) An upper triangular system of equations always has a solution, which can be computed
by back-substitution.
(e) Solving an upper triangular system of equations involving nequations and nunknowns
costs n2/2 + O(n)arithmetic operations.
2. Read Algorithm 2.1 in the text book for forward substitution that solves a lower triangular
system of equations Ly =b. Study the Matlab M-file forwardsubs.m provided in the
course directory to see how it is implemented. Now read Algorithm 2.2 for back-substitution
in the book that solves an upper triangular system of equations Ux =b, and write a Matlab
program implementing it as an M-file.
You should turn in a hard copy of your M-file and also email the M-file as a plain ascii file
to me at [email protected].
3. Use the Matlab program you wrote in the previous problem to solve systems of equations
with random upper triangular matrices of order 100,200,500, and 1000. Use the follow-
ing commands to generate the upper triangular matrix and the right-hand side vector. (The
sentences in parentheses are comments that explain the Matlab commands.)
1
pf2

Partial preview of the text

Download 3 Question for Computational Methods and Software - Assignment 2 | CS 417 and more Assignments Computer Science in PDF only on Docsity!

CS 417/517 Computational Methods and Software

Spring 2004 HW 2 Assigned: Thurs Jan 29, 2004; Due: Thurs Feb 5, 2004

Homework problems will be posted in the course directory: www.cs.odu.edu/˜pothen/Courses/CS417. If any corrections are found to be neces- sary, they will be posted in this directory as well. You must show your work to receive credit for your answers. In problems where you are asked to give reasons, an answer without a stated reason will receive no credit.

  1. Answer the following questions as true or false, giving a reason for your answer.

(a) Floating point addition is commutative: the order in which two numbers are written when they are added makes no difference to the result; i.e., a + b = b + a. (b) Floating point addition is associative: the order in which three numbers are added, makes no difference to the result; i.e., (a + b) + c = a + (b + c). (c) If two real numbers can be exactly represented as floating point numbers, then their exact sum can always be represented as a floating point number without any rounding errors. (d) An upper triangular system of equations always has a solution, which can be computed by back-substitution. (e) Solving an upper triangular system of equations involving n equations and n unknowns costs n^2 /2 + O(n) arithmetic operations.

  1. Read Algorithm 2.1 in the text book for forward substitution that solves a lower triangular system of equations Ly = b. Study the Matlab M-file forwardsubs.m provided in the course directory to see how it is implemented. Now read Algorithm 2.2 for back-substitution in the book that solves an upper triangular system of equations U x = b, and write a Matlab program implementing it as an M-file. You should turn in a hard copy of your M-file and also email the M-file as a plain ascii file to me at [email protected].
  2. Use the Matlab program you wrote in the previous problem to solve systems of equations with random upper triangular matrices of order 100 , 200 , 500 , and 1000. Use the follow- ing commands to generate the upper triangular matrix and the right-hand side vector. (The sentences in parentheses are comments that explain the Matlab commands.)

n= 100; (change this to the values you need in future steps.) A = sprand(n, n, 0.1); (creates a sparse random matrix of order n.) A = A + eye(n); (adds one to each diagonal element.) U = triu(A); (extracts the upper triangular part of A.) b = sum(U, 2); (adds the rows of U together to create b.) e= ones(n,1); (creates a column vector of n ones.) spy(U); (shows a picture of the matrix U.)

Solve the system of equations U x = b using your M-file. If the solution is computed in the vector x, then you can plot the difference between it and the vector of all ones by the Matlab command plot(x-e). Print the plot for each value of n, and submit it. Also, report the time taken by your program for back-substitution for each value of n, using the command cputime.

P.S. If you are not able to get your program for back-substitution working, then you can do this problem with the forward-substitution code that I have provided in forwardsubs.m. But now create a lower triangular matrix, and make other changes as needed.