Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 12.2, Problem 5E
a.
To determine
To explain: Why the normalized simultaneous iterations fail for the given matrix.
b.
To determine
To explain: Why the normalized simultaneous iterations fail for the given matrix.
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optimizaton theory
B1 The x distribution is a special case of Gamma distribution (not to be confused with gamma
function; see below). The density function of the Gamma distribution with parameters
and k is given by
where
-1
e
-x/0
(x) =
=
г(k) Øk
if x > 0, and
otherwise,
г(k) = √ ₁
k-1-x dx
x' e
is the gamma function.
(a) For every k ≥ 1, 0 > 0, find the mode of the density. Hint: The algebra can be
simplified by appropriate use of logarithms.
~
Now suppose that X1,..., Xn id Exp(\) and that we have a prior belief in A which is
consistent with a prior distribution X. Gamma(a, b), for some a, ß, i.e. the prior density
of is
Baxa-1-BA
T(a)
e
=
so 01/ẞ and k = a.
(b) Write down the likelihood, and show that the posterior distribution for \ is also a
Gamma distribution, but with parameters a +n and B + Σ Xi.
(c) Find the mode of the posterior distribution and examine the behaviour as n → ∞.
SCIE 211 Lab 3: Graphing and DataWorksheetPre-lab Questions:1. When should you use each of the following types of graphs? Fill answers in the table below.Type of Graph Used to showLine graphScatter plotBar graphHistogramPie Chart2. Several ways in which we can be fooled or misled by a graph were identified in the Lab 3Introduction. Find two examples of misleading graphs on the Internet and paste them below. Besure to identify why each graph is misleading.
Data Charts:Circumference vs. Diameter for circular objectsDiameter Can 1 (cm) Can 2 (cm) Can 3 (cm)Trial 1Trial 2Trial 3MeanCircumference Can 1 (cm) Can 2 (cm) Can 3 (cm)Trial 1Trial 2Trial 3MeanScatter Plot Graph – Circumference Vs. DiameterIdentify 2 points of the Trendline.Y1 = ________ Y2 = _________X1 = ________ X2 = _________Calculate the Slope of the Trendline =
Post-lab Questions:1. Answer the questions below. You will need to use the following equation to answer…
Chapter 12 Solutions
Numerical Analysis
Ch. 12.1 - Find the characteristic polynomial and the...Ch. 12.1 - Find the characteristic polynomial and the...Ch. 12.1 - Prob. 3ECh. 12.1 - Prove that a square matrix and its transpose have...Ch. 12.1 - Assume that A is a 33 matrix with the given...Ch. 12.1 - Assume that A is a 33 matrix with the given...Ch. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Let A=[ 1243 ] . (a) Find all eigenvalues and...Ch. 12.1 - Let A=[ 2113 ] . Carry out the steps of Exercise 9...
Ch. 12.1 - If A is a 66 matrix with eigenvalues -6, -3, 1, 2,...Ch. 12.1 - Prob. 1CPCh. 12.1 - Prob. 2CPCh. 12.1 - Prob. 3CPCh. 12.1 - Prob. 4CPCh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Call a square matrix stochastic if the entries of...Ch. 12.2 - Prob. 5ECh. 12.2 - (a) Show that the determinant of a matrix in real...Ch. 12.2 - Decide whether the preliminary version of the QR...Ch. 12.2 - Prob. 8ECh. 12.2 - Prob. 1CPCh. 12.2 - Prob. 2CPCh. 12.2 - Prob. 3CPCh. 12.2 - Prob. 4CPCh. 12.2 - Prob. 5CPCh. 12.2 - Prob. 6CPCh. 12.2 - Prob. 7CPCh. 12.2 - Verify the page rank eigenvector p for Figure...Ch. 12.2 - Prob. 2SACh. 12.2 - Prob. 3SACh. 12.2 - Prob. 4SACh. 12.2 - Set q=0.15 . Suppose that Page 2 in the Figure...Ch. 12.2 - Prob. 6SACh. 12.2 - Design your own network, compute page ranks, and...Ch. 12.3 - Find the SVD of the following symmetric matrices...Ch. 12.3 - Prob. 2ECh. 12.3 - Prob. 3ECh. 12.3 - (a) Prove that the ui , as defined in Theorem...Ch. 12.3 - Prove that for any constants a and b, the nonzero...Ch. 12.3 - Prob. 6ECh. 12.3 - Prob. 7ECh. 12.3 - Prove that for any constants a and b, the nonzero...Ch. 12.4 - Use MATLAbS svd command to find the best rank-one...Ch. 12.4 - Prob. 2CPCh. 12.4 - Find the best least squares approximating line for...Ch. 12.4 - Find the best least squares approximating plane...Ch. 12.4 - Prob. 5CPCh. 12.4 - Continuing Computer Problem 5, add code to find...Ch. 12.4 - Use the code developed in Computer Problem 6 to...Ch. 12.4 - Import a photo, using MATLABs imread command. Use...
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