SET A = a + 4b IF A = 0 SET A TO 20 SET B...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
SET A = a² + 4b IF A = 0 SET A TO 20 SET B TO B = 2x₁/a - xo SET TO (A + Bn)(a/2)" x RETURN x ELSE SET 0₁ TO (a + √A)/2 SET 0₂ TO (a - √A)/2 SET A TO your value of A from 3(a). SET B TO your value of B from 3(a). SET TO A0+ B02 RETURN x 6. In this question, the rounding errors incurred by the exact-formula algorithm are analysed. You may assume that a, b, xo, ₁ are all integers no larger in magnitude than 106 and that the computer is using double precision. (a) Each time a computer calculates a value x which is not in the registry, instead of storing the true value x, it stores the computed value æº. Set d to be the relative rounding error incurred by doing the computation i.e. da = xc - - I Express in terms of x and d, and give bounds on d in terms of machine precision t (so t = 52 for double precision). [2] (b) Suppose that a and b are such that A = 0. By expressing the values computed at each stage in the form given in (a), show that the total rounding error incurred by the exact-formula algorithm is O(2-t), so the algorithm does not significantly amplify the rounding errors. (c) Analyse the rounding errors incurred by the exact-formula algorithm when A ‡ 0. (d) For which values of a, b, x0, x₁, n would you expect this algorithm to be the most susceptible to rounding errors? Is the size of the error a concern in this case? [5] [7] [4] SET A = a² + 4b IF A = 0 SET A TO 20 SET B TO B = 2x₁/a - xo SET TO (A + Bn)(a/2)" x RETURN x ELSE SET 0₁ TO (a + √A)/2 SET 0₂ TO (a - √A)/2 SET A TO your value of A from 3(a). SET B TO your value of B from 3(a). SET TO A0+ B02 RETURN x 6. In this question, the rounding errors incurred by the exact-formula algorithm are analysed. You may assume that a, b, xo, ₁ are all integers no larger in magnitude than 106 and that the computer is using double precision. (a) Each time a computer calculates a value x which is not in the registry, instead of storing the true value x, it stores the computed value æº. Set d to be the relative rounding error incurred by doing the computation i.e. da = xc - - I Express in terms of x and d, and give bounds on d in terms of machine precision t (so t = 52 for double precision). [2] (b) Suppose that a and b are such that A = 0. By expressing the values computed at each stage in the form given in (a), show that the total rounding error incurred by the exact-formula algorithm is O(2-t), so the algorithm does not significantly amplify the rounding errors. (c) Analyse the rounding errors incurred by the exact-formula algorithm when A ‡ 0. (d) For which values of a, b, x0, x₁, n would you expect this algorithm to be the most susceptible to rounding errors? Is the size of the error a concern in this case? [5] [7] [4]
Expert Answer:
Related Book For
Income Tax Fundamentals 2013
ISBN: 9781285586618
31st Edition
Authors: Gerald E. Whittenburg, Martha Altus Buller, Steven L Gill
Posted Date:
Students also viewed these programming questions
-
I have a c code I need to write comments for the code */ #include #include "foc_sp20.h" int list(void); double task3(void); void task4(double probability); void task5(void); int main() {...
-
I just dont understand these financial statements at all! exclaimed Mr. Elmo Knapp. Mr. Knapp explained that he had turned over management of Racketeer, Inc., a division of American Recreation...
-
I just need Part C., wouldn't the extra income per year be $25,000? I need an explanation if possible please for the extra income part, thank you! You are deciding whether or not to go to attend a...
-
Given that y = x 2 , find the image of the curve y = x 2 after each of the following combinations of transformations. a. A stretch in the y-direction with factor 3 followed by a translation by the...
-
1. What types of documentation are needed for this application? 2. During application development, what steps should the IT staff follow to develop a structure chart? 3. What suggestions do you have...
-
Graph each horizontal parabola, and give the domain and range. x- 4 =;(y 1)
-
The November cash records of Stenback, Inc., follow: Stenbacks Cash account shows the balance of $6,172 on November 30. On November 30, Stenback received the following bank statement: Additional data...
-
Arthur Katz testified for the U.S. government in a stock manipulation case. He also pled guilty and testified against three of his law partners in an insurance fraud case. He received a six-month...
-
If the cost of equity capital is 15% p.a., the market value of equity is $5 million, the company tax rate is 30%, the cost of debt is 12% p.a. and y = 0.60, what is the cost of capital?
-
Consider the idealized, symmetric two-cell wing box shown in the figure below. The area enclosed by the semi-elliptical web 45 is 51,500 mm. The shear modulus of the material is G = 27 GPa....
-
find the domain and range of f^-1(x) if f(x) is defined as follows: f(x)= 8sqrt(x-9) +2 f(x)= (x+2)/(x-3) f(x)= 11- sqrt(7x-5) f(x)= (3x-4)/(x+2)
-
A company knows that it will need to borrow $1.5 million in three months time for a twelve-month period. It can borrow funds at LIBOR + 50 basis points. LIBOR rates today are at 5% but the company's...
-
Write a 350- to 700-word report in which you respond to each of the prompts below. Consider what you know about consumer behavior and the importance of innovation in health care in your responses....
-
Explain three reasons why corporate risk is important even if a firm's stockholders are well diversified.
-
High Growth Thinking Exercise Discuss cryptocurrency and blockchain technology and how they might impact the economy. Discuss some of the ethical considerations associated with AI and Automation and...
-
18.5 FL The Orphane Company buys raw materials from an outside supplier at $40 per unit; total annual needs are 6,400 units. The material is used evenly throughout the year. Order costs are $100 per...
-
Question 40 T.L.C. Enterprises just revised its capital structure from a debt-equity ratio of 0.30 to a debt-equity ratio of 0.45. The firm's shareholders who prefer the old capital structure should:...
-
Represent each of the following combination of units in the correct SI form using an appropriate prefix: (a) m/ms, (b) k m, (c) k s /mg, and (d) k m N.
-
Jerry made the following contributions during 2012: His synagogue (by check).....................................................$680 The Democratic Party (by check)...
-
Mike purchases a heavy-duty truck (5-year class recovery property) for his delivery service on April 30, 2012. The truck is not considered a passenger automobile for purposes of the listed property...
-
Sherry rents her vacation home for 6 months and lives in it for 6 months during the year. Her gross rental income during the year is $4,000. Total real estate taxes for the home are $950, and...
-
The following questions relate to use of audit sampling for tests of transaction classes. Select the best response. a. Given random selection, the same sample size, and the same tolerable rate for...
-
For each one of the following statements indicate whether the statement is true or false. a. When the auditor's approach to substantiating an account balance is to apply an audit procedure to less...
-
The following questions relate to the selection of audit samples. Select the best response. a. Which of the following statistical selection techniques is least desirable for use by an auditor? 1....
Study smarter with the SolutionInn App