Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Textbook Question
Chapter 4.2, Problem 8CP
The file scrippsy. txt, available from the textbook website. is a list of 50 numbers which represent the concentration of atmospheric carbon dioxide, in parts per million by volume (ppv), recorded at Mauna Loa, Hawaii, each May 15 of the years 1961 to 2010. The data is part of a data collection effort initiated by Charles Keeling of the Scripps Oceanographic Institute (Keeling et al. (2001]). Subtract the background level 279 ppm as in Computer Problem 4, and fit the data to an exponential model. Plot the data along with the best fit exponential function, and report the RMSE.
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The table below represents approximate data obtained from the United States Geological
Survey (USGS).
Volcano Eruption Data
Approximate Number of
Eruptions Since 2200 B.C.
(unless otherwise indicated)
Year of
Average
Eruption Predicted
Rate
Next
Volcano
Location
Last
Eruption
Eruption
Mt. Adams
Washington
2
550 B.C.
Mt. Baker
Washington
1880
Glacier Peak
Washington
6.
1700
Mt. Hood
Oregon
3
1866
Hualalai
Hawaii
80
1801
Mt. Jefferson
Oregon
950
Kilauea
Hawaii
61 (since 1750)
2014
Lassen Peak
California
3
1917
Mauna Loa
Hawaii
33 (since 1843)
1984
Mt. Mazama
Oregon
1
2290 B.C.
Medicine Lake
Califormia
1080
Newberry
Oregon
2.
690
Mt. Ranier
Washington
11
1894
Mt. Shasta
California
7.
1786
Mt. St. Helens Washington
19
2008
1. Use the table to determine which state is most likely to be affected by an erupting voleano.
Hawaii would most likely be affected
2. Imagine you are a scientist. List six questions you would ask about the given data.
3. What method was used to collect this data? Why…
How sensitive to changes in water temperature are coral reefs? To find out, scientists examined data on sea surface temperatures, in degrees Celsius, and mean coral growth, in centimeters per year, over a several‑year period at locations in the Gulf of Mexico and the Caribbean Sea. The table shows the data for the Gulf of Mexico.
Sea surface temperature
26.726.7
26.626.6
26.626.6
26.526.5
26.326.3
26.126.1
Growth
0.850.85
0.850.85
0.790.79
0.860.86
0.890.89
0.920.92
(b) Find the correlation ?r step by step. Round off to two decimals places in each step. First, find the mean and standard deviation of each variable. Then, find the six standardized values for each variable. Finally, use the formula for ?r . Round your answer to three decimal places.
Chapter 4 Solutions
Numerical Analysis
Ch. 4.1 - Solve the normal equations to find the least...Ch. 4.1 - Find the least squares solutions and RMSE of the...Ch. 4.1 - Find the least squares solution of the...Ch. 4.1 - Let mn, let A be the mn identity matrix (the...Ch. 4.1 - Prove that the 2-norm is a vector norm. You...Ch. 4.1 - Let A be an nn nonsingular matrix. (a) Prove that...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best line through the set of data points,...Ch. 4.1 - Find the best parabola through each data point set...Ch. 4.1 - Find the best degree 3 polynomial through each set...
Ch. 4.1 - Assume that the height of a model rocket is...Ch. 4.1 - Given data points...Ch. 4.1 - Form the normal equations, and compute the least...Ch. 4.1 - Prob. 2CPCh. 4.1 - Prob. 3CPCh. 4.1 - Prob. 4CPCh. 4.1 - 5. A company test-markets a new soft drink in 22...Ch. 4.1 - What is the slope of the parabola y=x2on[ 0,1 ] ?...Ch. 4.1 - Find the least squares (a) line (b) parabola...Ch. 4.1 - Let A be the 10n matrix formed by the first n...Ch. 4.1 - Prob. 9CPCh. 4.1 - The following data, collected by U.S. Bureau of...Ch. 4.2 - Fit data to the periodic model...Ch. 4.2 - Fit the data to the periodic models...Ch. 4.2 - Fit data to the exponential model by using...Ch. 4.2 - Prob. 4ECh. 4.2 - Fit data to the power law model by using...Ch. 4.2 - Prob. 6ECh. 4.2 - Fit the monthly data for Japan 2003 oil...Ch. 4.2 - Prob. 2CPCh. 4.2 - Prob. 3CPCh. 4.2 - Prob. 4CPCh. 4.2 - Prob. 5CPCh. 4.2 - Prob. 6CPCh. 4.2 - Prob. 7CPCh. 4.2 - The file scrippsy. txt, available from the...Ch. 4.2 - The file scrippsm.txt, available from the textbook...Ch. 4.3 - Apply classical Gram-Schmidt orthogonalization to...Ch. 4.3 - Apply classical Gram-Schmidt orthogonalization to...Ch. 4.3 - Apply modified Gram--Schmidt orthogonalization to...Ch. 4.3 - Apply modified Gram-Schmidt orthogonalization to...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Prob. 7ECh. 4.3 - Find the QR factorization and use it to solve the...Ch. 4.3 - Prove that a square matrix is orthogonal if and...Ch. 4.3 - Prove that the product of two orthogonal mm...Ch. 4.3 - Show that the Gram-Schmidt orthogonalization of an...Ch. 4.3 - Show that the Householder reflector method for the...Ch. 4.3 - Let P be the matrix defined in (4.29). Show (a)...Ch. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Write a MATLAB program that implements the...Ch. 4.3 - Apply the classical Gram-Schmidt, modified...Ch. 4.3 - Prob. 3CPCh. 4.3 - Write a MATLAB program that implements (a)...Ch. 4.3 - Prob. 5CPCh. 4.3 - Use the MATLAB QR factorization to find the least...Ch. 4.3 - Prob. 7CPCh. 4.3 - Let x1,...,x11be11 be evenly spaced points in...Ch. 4.4 - Solve Ax=b for the following A and b=[ 1,0,0 ]T,...Ch. 4.4 - Prob. 2ECh. 4.4 - Let A=[ 10a1301a23001 ]. Prove that for any x0 and...Ch. 4.4 - Prob. 4ECh. 4.4 - Prob. 1CPCh. 4.4 - Prob. 2CPCh. 4.4 - Prob. 3CPCh. 4.4 - Let A be the matrix from Computer Problem 3, but...Ch. 4.4 - Prob. 5CPCh. 4.5 - The Gauss-Newton Method can be applied to find the...Ch. 4.5 - Prob. 2ECh. 4.5 - Prove that the distance from a point (x,y) to a...Ch. 4.5 - Prob. 4ECh. 4.5 - Find the matrix Dr needed for the application of...Ch. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Prob. 1CPCh. 4.5 - Prob. 2CPCh. 4.5 - Prob. 3CPCh. 4.5 - Prob. 4CPCh. 4.5 - Prob. 5CPCh. 4.5 - Prob. 6CPCh. 4.5 - Prob. 7CPCh. 4.5 - Prob. 8CPCh. 4.5 - Prob. 9CPCh. 4.5 - Prob. 10CPCh. 4.5 - Prob. 11CPCh. 4.5 - Prob. 1SACh. 4.5 - Prob. 2SACh. 4.5 - Prob. 3SACh. 4.5 - Prob. 4SACh. 4.5 - Now repeat Step 4 with a more tightly grouped set...Ch. 4.5 - Decide whether the GPS en-or and condition number...
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