Discuss the parallel performance of the lu factorization

Assignment Help Theory of Computation
Reference no: EM13923511

You are provided with a program matrix_serial . c to solve a linear system of equations Ax = b. The code includes routines to initialize A and b, compute the LU factorization of A, and solve triangular systems with lower and upper triangular matrices. The main program uses these routines to compute the solution of the system Ax = b by computing A = LU, and solving Ly = b for y, followed by Ux = y for x. Instructions to compile and execute the code are included in the file.

You need to parallelize the routines for computing LU factorization and solving the triangular systems using pthreads. The file should be named matrix . c.

1. You need to parallelize the routines for computing LU factorization and solving the triangular systems using pthreads. The file should be named matrix . c. A total of 20 points are reserved for performance of the code: speedup obtained by the multithreaded code and the overall execution time will be considered when awarding these points.

2. Execute the code for n= 212 with p chosen to be 2k, for k = 0, 1,...,6. Plot execution time versus p to demonstrate how time varies with the number of threads. Use logarithmic scale for the x-axis. Plot speedup versus p to demonstrate the change in speedup with p.

3. Discuss the parallel performance of the LU factorization routine and the triangular solver routines. Comment on the observed performance and the possible reasons for the observations.

4. You will receive bonus points equal to the amount the sum of speedups observed in the following routines - LU factorization, lower triangular solve, and upper triangular solve - exceeds 2.0. Speedup is computed as the speed improvement achieved by each routine over the execution time of the routine reported by matrix_serial . c for a single run. Bonus points are subject to a maximum of 10 points. Total speedup value will be rounded. Individual routine speedup values lower than 1.0 will be raised to 1.0 to compute bonus points. For example, a speedup of 3.5, 2.1, and 0.7, respectively, in the three routines is awarded 5 bonus points. In your submission, you need to specify the input arguments to the executable that produce the best speedup. Also indicate the speedup you observe in each of the routines. Compilation will be done using icc with default optimization.

Attachment:- hw4.txt

Reference no: EM13923511

Questions Cloud

Compute the black-scholes option and hedge ratio values : Compute the Black-Scholes option and hedge ratio values for the series of hypothetical current stock price levels shown in Exhibit 22.12. Explain why the values in Part a differ from those shown in Exhibit 22.12.
Research in the students academic specialization : Critique existing research and design a methodologically sound approach to research in the student's academic specialization(s).
In revelation the seven bowl judgments : The last book of the bible describes itself as a "revelation of Jesus Christ" (1:1) an expression that functions as a title for the entire book.According to 1 John, we can know for sure that we have eternal life for "God has given us eternal life..
Manufactures and distributes toys throughout south east : Pearl Products Limited of Shenzhen, China, manufactures and distributes toys throughout South East Asia. Three cubic centimeters (cc) of solvent H300 are required to manufacture each unit of Super mix, one of the company's products.
Discuss the parallel performance of the lu factorization : Discuss the parallel performance of the LU factorization routine and the triangular solver routines. Comment on the observed performance and the possible reasons for the observations.
Find the variance of the probability distribution. : What is the probability that at least two of the three vice presidents can attend the meeting?
Relationship-specific exchange in contractural environments : When relationship-specific exchange occurs in complex contractural environments, the best way to purchase inputs is through:
Arcs in a project network indicate : Activities G, P, and R are the immediate predecessors for activity W. If the earliest finish times for the three are 12, 15, and 10, then the earliest start time for W
Morganton company makes one product : Morganton Company makes one product and it provided the following information to help prepare the master budget for its first four months of operations:

Reviews

Write a Review

 

Theory of Computation Questions & Answers

  Develop a website - an education consulting firm

Develop a Website: An education consulting firm would like to develop a career oriented website for guide them for higher education in Australia.

  Write a g code program to machine

Write a G code program to machine the below part on the CNC turning machine. Simulate the code using any free simulation package (simulation screenshots have to be included in report)

  Is the given grammar left or right recursive

Is the given grammar left or right recursive - describe these in detail because I am having a hard time trying to figure this all out.

  Prove the given proposition using proof contradiction

Prove the given proposition using Proof Contradiction.

  Write grammar for language consisting of strings

Write a grammar for the language consisting of strings that have n copies of the letter a followed by same number of copies of the letter b, where n>0

  Joe must decide how he will answer bills invitation to join

joe must decide how he will answer bills invitation to join him and his family on their yacht. complete the following

  1- when organization have a balance of both management and

1- when organization have a balance of both management and leadership and goals and challenges have been met how do we

  Design a dfa to recognize language l

Design a DFA to recognize L and write a program that implements your DFA - you should check the ASCII code of each character of the string and process on the DFA accordingly.

  Construct a dfa that recognizes languages

Construct a DFA that recognizes each of the following languages. Unless otherwise noted we are assuming that ω ∈ {0,1}*. (A drawing of a state diagram is sufficient.)

  Decrypt the message without computing bobs private key

Decrypt the message without computing Bobs private key. Just look at the cipher text and use the fact that there are only very few masking keys and a bit of guesswork.

  Question 1 given the productionss-gt sa aaa absa-gt acaa

question 1. given the productions.s-gt sa aaa absa-gt acaa list the parse table. is the grammar ll1 in this form? if

  Write the predicate logic

Write the predicate singleChild(Name) which finds the name of single children - For this problem single children means no other child has the same father and mother.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd