Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Textbook Question
Chapter 7.3, Problem 3CP
Carry out the steps of Computer Problem 1, using the Finite Element Method.
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Problem 4.
The number of memory chips M needed in a personal computer depends
on how many application programs, A, the owner wants to run simulta-
neously. The number of chips M and the number of application programs
A are described by
(4 chips for 1 program,
4 chips for 2 programs,
[0.1(5 – a) a = 1,2,3, 4,
M =
PA(a) =
6 chips for 3 programs,
8 chips for 4 programs,
otherwise.
(1)
(a) What is the expected number of programs uA = E[A]?
(b) Express M, the number of memory chips, as a function M = g(A) of
the number of application programs A.
(c) Find E[M] = E[g(A)]. Does E[M] = g(E[A])?
(d) Find Variance of A and M
1. Solve the multiplication problem
d b.
96
X 8
in three different ways: by using the standard
brs algorithm, by using the partial-products algorithm,
and by writing the numbers in expanded forms and
using properties of arithmetic. For each of the three
methods, discuss how the steps in that method are
related to the steps in the other methods.
01 oid
с.
6. а.
Chapter 7 Solutions
Numerical Analysis
Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Apply the Shooting Method to the linear BVPs....
Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CPCh. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SACh. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SACh. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CPCh. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...
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- Evaluate problem 23 using theorem 4arrow_forwardPlease note this is a block multiplication problem…arrow_forwardProblem 2. The following algorithm which is used to evaluate a polynomial anr" + an-17"-1 +……+a1x + ao at r = c is expressed in pseudocode as follows: procedure polynomial evaluation (c, ao, - - - ,an : real numbers) y:= an for i := 1 to n y := y *c+ an-i return y {y = an" + an-17"-1 + ...+aįx+ ao}. where the final value of y is the value of the polynomial at r = c. (a) Evaluate 12r + 3r3 – 52² + 7x – 8 at r = -1 by working through each step of the a showing the values assigned at each assignment step CLEARLY. Answers with missing it indices, etc. will not be taken into account.arrow_forward
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- - 5 0 -4 -5 3-4 Compute: 4 1 -4 –5 1 5 1 -1 4 4 -1arrow_forwardshow that the computing formula for s2 on page 44 is equivalent to the one used to define s2 on page 37arrow_forwardProblem 2. The following algorithm which is used to evaluate a polynomial Anx" + an-1x"–1 +...+ ajx+ ao at x = c is expressed in pseudocode as follows: procedure polynomial evaluation (c, ao, · , an : real numbers) y := an for i := 1 to n y := y * c + ɑn-i return y {y = anx" + an-1x"-1 +...+ a1x + ao}. where the final value of y is the value of the polynomial at x = c. (a) Evaluate 12x4 + 3x³ – 5a² + 7x – 8 at x = -1 by working through each step of the algorithm showing the values assigned at each assignment step CLEARLY. Answers with missing iterations, indices, etc. will not be taken into account. (b) How many additions and multiplications take place in the evaluation of a polynomial of degree n? Briefly explain. (Do not include the additions needed to increment the loop variable i.) (c) One can represent polynomials using nested multiplications, that is successively taking x as a common factor in the remaining polynomials of decreasing degrees, for example 3x3 + 2x? + 5x +4= x(x(3x…arrow_forward
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