. An implicit finite difference scheme solves for an n x 1 vector x using an...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
. An implicit finite difference scheme solves for an n x 1 vector x using an n x n coefficient matrix A and an n x 1 force vector b. The governing equation is Ax = b and can be solved in MATLAB using x A\b. Here, we want to test the computational complexity for x =A\b in a specific scheme where A and b are set up as follows: A(i, j) = 0 except: o o o o O A(i, j) = -1 ifj=i-1 or j=i+1 A (i, j) = 2 ifj equals i A(1,1)= 1 A(n,n) = 1 Also, b(i) = 0 except b(1) = b(n) equals 1. a. Determine theoretically how to determine the computational complexity exponent p based on two points (n₁, t₁) and (n₂, t₂). b. Plot the time required using 50 ≤ n ≤ 100 for x A\b [hint: initialize A and b arrays using A zeros (n) and b = zeros (n,1), and then overwrite specific values of A and b]. Pick two points that avoid outliers and estimate the computational complexity. . An implicit finite difference scheme solves for an n x 1 vector x using an n x n coefficient matrix A and an n x 1 force vector b. The governing equation is Ax = b and can be solved in MATLAB using x A\b. Here, we want to test the computational complexity for x =A\b in a specific scheme where A and b are set up as follows: A(i, j) = 0 except: o o o o O A(i, j) = -1 ifj=i-1 or j=i+1 A (i, j) = 2 ifj equals i A(1,1)= 1 A(n,n) = 1 Also, b(i) = 0 except b(1) = b(n) equals 1. a. Determine theoretically how to determine the computational complexity exponent p based on two points (n₁, t₁) and (n₂, t₂). b. Plot the time required using 50 ≤ n ≤ 100 for x A\b [hint: initialize A and b arrays using A zeros (n) and b = zeros (n,1), and then overwrite specific values of A and b]. Pick two points that avoid outliers and estimate the computational complexity.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
Do some amendment and enhance the given research paper: Table of Content Abstract..3 Action Research.4 Research Methodology and Design...5 Literature Review: NoSQL Database7 Proposal.7 Iteration 1..8...
-
In Example 8.2.7 we saw an example of a one-sided Bayesian hypothesis test. Now we will consider a similar situation, but with a two-sided test. We want to test H0: = 0 versus H1: 0, and we...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Answer the following question based on the information presented for Cloud 9 in the appendix to this text and the current and earlier chapters. You should also consider your answers to the case study...
-
Delta Company, a U.S. MNC, is contemplating making a foreign capital expenditure in South Africa. The initial cost of the project is ZAR10,000. The annual cash flows over the five-year economic life...
-
The graph of a function is shown below. (a) Sketch '. (b) Use the graphs to estimate (c) Explain the answers you gave in part (b). -4 -2 6 4 2 -2 y f ++ +xx 2 4
-
What is a pump? What are its functions?
-
The State of Ohio decides that Ohio's landfills are becoming too full at too rapid a pace, so it passes a law banning the import of waste generated out of state. Several landfill operators have...
-
Title IV of Civil Rights Act applied to coaching https://www2.ed.gov/about/offices/list/ocr/docs/interath.html Equal Opportunity In Intercollegiate Athletics: RequirementsUnder Title IX of the...
-
Consider a system of particles uniformly distributed in space, with a constant particle number density n 0 , and characterized by a velocity distribution function f(v) such that where K 0 is a...
-
A mall charges 25 for the first hour or a fraction of an hour as parking fee. An additional 25 is charged for every additional hour, or a fraction of an hour of parking. The parking area operates...
-
Jerry and Paula Ranch are finally retired. All of their years of hard work have finally paid off. They purchased a second home on the beach decades ago. It was a teardown, and they have slowly...
-
A nickel crystals work function is measured to be 5.22 eV at 25C. As the temperature increases by 300C, the work function drops by 50 meV. By how much does this shift the threshold wavelength for...
-
One molecule of ATP provides 0.30 eV when it is used to power cellular processes. Photosynthesis in a typical plant requires 8 photons at 550 nm to produce 1 molecule of ATP. What is the overall...
-
A crystal sample of bacteriorhodpsin, a light-sensitive protein found in halobacteria that responds to light energy, has crystal planes separated by 0.20 nm. If a beam of 11 keV x rays illuminates a...
-
A study of photosynthesis in phytoplankton in the open ocean used short pulses of laser light to trigger photosynthetic reactions. The investigators system used 0.10 mW pulses of 640 nm laser light...
-
PROVE that for any convex polygon with three angles whose sum is 180 , then the polygon must be a triangle.
-
Evaluate how many lines there are in a true rotational spectrum of CO molecules whose natural vibration frequency is w = 4.09 1014 s1 and moment of inertia I = 1.44 1039 g cm2.
-
Which of the following quadratic functionals possess a unique minimizer among all functions satisfying the indicated boundary conditions? Find the minimizer if it exists. a. b. c. d. e. a( 1 ) =...
-
A steady state fluid flow has velocity vector v = (-2y, 2x, z)T. Describe the motion of the fluid particles as governed by the differential equation dx/dt = v
-
Prove that each of the following formulas for (v. tv) defines an inner product on R3. Verify all the inner product axioms in careful detail: (a) V1W1 + 2V2w2 + 3v3w3 (b) 4v1w1 + 2 v1w2 + 2v2wi +4v2W2...
-
Define family law and identify the kinds of issues that are addressed in a family law practice.
-
Describe the role of a paralegal in a family law practice.
-
Identify the kinds of resources included in a basic family law library.
Study smarter with the SolutionInn App