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Exam 2 Math 3607, Summer 2021 [NAME.NUMBER] Table of Contents Instructions
Signature
Problem 1 (PLU Factorization by Hand)
Problem 2 (Catastrophic Cancellation)
Problem 3 (Least Squares for Periodic Data)
Problem 4 (Visualization of Matrix Norms in 3-D)
Functions Used
Visualization of Matrix Norms (Problem 4) Instructions Rename this file to “exam2_Lastname_Firstname.mlx” (e.g. “exam2_Kim_TaeEun.mlx”). In addition, type in your OSU name.number at the top of this document where it says [NAME.NUMBER]. Failure to do so will result in point deduction. Insert your signature (picture file) in the next section. Submission without a signature WILL NOT be accepted. Fill in the live script with your answers. Lengthy explanation of your code or justification involving many mathematical symbols may be typed or handwritten. Do whichever is more convenient for you. All MATLAB functions written for the exam must be included at the end of this file. Once completed, re-run the entire live script to ensure that requested outputs and figures are properly generated. Export to pdf. Do NOT manually modify the generated pdf file. Upload mlx and pdf files. Do not use any external m-files. Your submission must be self-contained. Signature Upon reading all the statements on the front page of the exam, please insert your signature (as a picture file) down below. Submission missing signature WILL NOT be accepted. [INSERT YOUR SIGNATURE (picture file)] Problem 1 (PLU Factorization by Hand) Type your solutions or insert your hand-written work here. Problem 2 (Catastrophic Cancellation) (a) (b) (c) (d)
Problem 3 (Least Squares for Periodic Data) (a) Download the data file pressuredata.mat onto the same folder as this mlx file. Then load it into MATLAB using load pressuredata as shown below. This creates two vectors t and y containing time and blood pressure data, respectively. Use them to regenerate the plot load pressuredata
% Make a labeled plot.
(b) (c) (d) Problem 4 (Visualization of Matrix Norms in 3-D) (a) Complete the function visMatrixNorms3D under “Functions Used”. (b) Run the following block. A = [2 0 0;
0 cos(pi/12) -sin(pi/12);
0 sin(pi/12) cos(pi/12)];
visMatrixNorms3D(A, 1);
visMatrixNorms3D(A, 3/2);
visMatrixNorms3D(A, 2);
visMatrixNorms3D(A, 4); Depending on how you write the code, you may need to use clf or hold off in between function calls. Functions Used Visualization of Matrix Norms (Problem 4) function norm_A = visMatrixNorms3D(A, p)
%% Basic checks
if size(A,1)~=3 || size(A,2)~=3
error(‘A must be a 3-by-3 matrix.’)
elseif p < 1
error('p must be >= 1.’)
end
%% Step 1: Initialization
nr_th = 41; nr_ph = 31;
th = linspace(0, 2*pi, nr_th);
ph = linspace(0, pi, nr_ph);
[T, P] = meshgrid(th, ph);
x1 = cos(T).*sin(P);
x2 = sin(T).*sin(P);
x3 = cos(P);
X = [x1(:), x2(:), x3(:)]’;
%% Step 2: [FILL IN] Normalize columns of X into unit vectors
%% Step 3: [FILL IN] Form Y = A*X and then calculate norms of columns of Y
%% Step 4: [FILL IN] Calculate p-norm of A (approximate)
%% Step 5: [FILL IN] Generate surface plots
end
manual code ready 0.4 true true 0 31 31
2021-06-24T03:38:05Z 2021-07-15T00:39:26Z
application/vnd.mathworks.matlab.code MATLAB Code R2020b
9.9.0.1444674 00949623-e3dc-4689-8f4a-c92f68c87f7c
9.9.0.1524771
R2020b
Update 2
Nov 03 2020
2207788044