Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 2.5, Problem 4E

Apply two steps of SOR to the systems in Exercise 2 after rearranging. Use starting vector [0,...,0] and ω = 1 and 1.2.

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The accompanying data shows the fossil fuels​ production, fossil fuels​ consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year    Fossil Fuels Production    Fossil Fuels Consumption    Total Energy Consumption1949    28.748    29.002    31.9821950    32.563    31.632    34.6161951    35.792    34.008    36.9741952    34.977    33.800    36.7481953    35.349    34.826    37.6641954    33.764    33.877    36.6391955    37.364    37.410    40.2081956    39.771    38.888    41.7541957    40.133    38.926    41.7871958    37.216    38.717    41.6451959    39.045    40.550    43.4661960    39.869    42.137    45.0861961    40.307    42.758    45.7381962    41.732    44.681    47.8261963    44.037    46.509    49.6441964    45.789    48.543    51.8151965    47.235    50.577    54.0151966    50.035    53.514    57.0141967    52.597    55.127    58.9051968    54.306    58.502    62.4151969    56.286…
The accompanying data shows the fossil fuels​ production, fossil fuels​ consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Develop line charts for each variable and identify the characteristics of the time series​ (that is,​ random, stationary,​ trend, seasonal, or​ cyclical).   What is the line chart for the variable Fossil Fuels​ Production?
The accompanying data shows the fossil fuels​ production, fossil fuels​ consumption, and total energy consumption in quadrillions of BTUs of a certain region for the years 1986 to 2015. Complete parts a and b. Year    Fossil Fuels Production    Fossil Fuels Consumption    Total Energy Consumption1949    28.748    29.002    31.9821950    32.563    31.632    34.6161951    35.792    34.008    36.9741952    34.977    33.800    36.7481953    35.349    34.826    37.6641954    33.764    33.877    36.6391955    37.364    37.410    40.2081956    39.771    38.888    41.7541957    40.133    38.926    41.7871958    37.216    38.717    41.6451959    39.045    40.550    43.4661960    39.869    42.137    45.0861961    40.307    42.758    45.7381962    41.732    44.681    47.8261963    44.037    46.509    49.6441964    45.789    48.543    51.8151965    47.235    50.577    54.0151966    50.035    53.514    57.0141967    52.597    55.127    58.9051968    54.306    58.502    62.4151969    56.286…

Chapter 2 Solutions

Numerical Analysis

Ch. 2.2 - Find the LU factorization of the given matrices....Ch. 2.2 - Find the LU factorization of the given matrices....Ch. 2.2 - Solve the system by finding the LU factorization...Ch. 2.2 - Solve the system by finding the LU factorization...Ch. 2.2 - Solve the equation Ax=b, where A=[...Ch. 2.2 - Given the 10001000 matrix A, your computer can...Ch. 2.2 - Assume that your computer can solve 1000 problems...Ch. 2.2 - Assume that your computer can solve a 20002000...Ch. 2.2 - Let A be an nn matrix. Assume that your computer...Ch. 2.2 - Use the code fragments for Gaussian elimination in...Ch. 2.2 - Add two-step back substitution to your script from...Ch. 2.3 - Find the norm A of each of the following...Ch. 2.3 - Find the (infinity norm) condition number of (a)...Ch. 2.3 - Find the forward and backward errors, and the...Ch. 2.3 - Find the forward and backward errors and error...Ch. 2.3 - Find the relative forward and backward errors and...Ch. 2.3 - Find the relative forward and backward errors and...Ch. 2.3 - Find the norm H of the 55 Hilbert matrix.Ch. 2.3 - (a) Find the condition number of the coefficient...Ch. 2.3 - (a) Find the condition number (in the infinity...Ch. 2.3 - (a) Find the (infinity norm) condition number of...Ch. 2.3 - (a) Prove that the infinity norm x is a vector...Ch. 2.3 - (a) Prove that the infinity norm A is a matrix...Ch. 2.3 - Prove that the matrix infinity norm is the...Ch. 2.3 - Prove that the matrix 1-norm is the operator norm...Ch. 2.3 - For the matrices in Exercise 1, find a vector x...Ch. 2.3 - For the matrices in Exercise 1, find a vector...Ch. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - For the nn matrix with entries Aij=5/(i+2j1), set...Ch. 2.3 - Carry out Computer Problem 1 for the matrix with...Ch. 2.3 - Let A be the nn matrix with entries Aij=| ij |+1 ....Ch. 2.3 - Carry out the steps of Computer Problem 3 for the...Ch. 2.3 - For what values of n does the solution in Computer...Ch. 2.3 - Use the MATLAB program from Computer Problem 2.1.1...Ch. 2.4 - Find the PA=LU factorization (using partial...Ch. 2.4 - Find the PA=LU factorization (using partial...Ch. 2.4 - Solve the system by finding the PA=LU...Ch. 2.4 - Solve the system by finding the PA=LU...Ch. 2.4 - Write down a 55 matrix P such that multiplication...Ch. 2.4 - (a) Write down the 44 matrix P such that...Ch. 2.4 - Change four entries of the leftmost matrix to make...Ch. 2.4 - Find the PA=LU factorization of the matrix A in...Ch. 2.4 - (a) Find the PA=LU factorization of A=[...Ch. 2.4 - (a) Assume that A is an nn matrix with entries |...Ch. 2.4 - Write a MATLAB program to define the structure...Ch. 2.4 - Plot the solution from Step 1 against the correct...Ch. 2.4 - Rerun the calculation in Step 1 for n=102k, where...Ch. 2.4 - Add a sinusoidal pile to the beam. This means...Ch. 2.4 - Rerun the calculation as in Step 3 for the...Ch. 2.4 - Now remove the sinusoidal load and add a 70 kg...Ch. 2.4 - If we also fix the free end of the diving board,...Ch. 2.4 - Ideas for further exploration: If the width of the...Ch. 2.5 - Compute the first two steps of the Jacobi and the...Ch. 2.5 - Rearrange the equations to form a strictly...Ch. 2.5 - Apply two steps of SOR to the systems in Exercise...Ch. 2.5 - Apply two steps of SOR to the systems in Exercise...Ch. 2.5 - Let be an eigenvalue of an nn matrix A. (a) Prove...Ch. 2.5 - Use the Jacobi Method to solve the sparse system...Ch. 2.5 - Use the Jacobi Method to solve the sparse system...Ch. 2.5 - Rewrite Program 2.2 to carry out Gauss-Seidel...Ch. 2.5 - Rewrite Program 2.2 to carry out SOR. Use =1.1 to...Ch. 2.5 - Carry out the steps of Computer Problem 1 with...Ch. 2.5 - Prob. 6CPCh. 2.5 - Using your program from Computer Problem 3. decide...Ch. 2.6 - Show that the following matrices are symmetric...Ch. 2.6 - Show that the following symmetric matrices are not...Ch. 2.6 - Prob. 3ECh. 2.6 - Show that the Cholesky factorization procedure...Ch. 2.6 - Prob. 5ECh. 2.6 - Find the Cholesky factorization A=RTR of each...Ch. 2.6 - Prob. 7ECh. 2.6 - Solve the system of equations by finding the...Ch. 2.6 - Prob. 9ECh. 2.6 - Find all numbers d such that A=[ 122d ] is...Ch. 2.6 - Prob. 11ECh. 2.6 - Prove that a principal submatrix of a symmetric...Ch. 2.6 - Solve the problems by carrying out the Conjugate...Ch. 2.6 - Solve the problems by carrying out the Conjugate...Ch. 2.6 - Carry out the conjugate gradient iteration in the...Ch. 2.6 - Prob. 1CPCh. 2.6 - Use a MATLAB version of conjugate gradient to...Ch. 2.6 - Solve the system Hx=b by the Conjugate Gradient...Ch. 2.6 - Solve the sparse problem of (2.45) by the...Ch. 2.6 - Prob. 5CPCh. 2.6 - Let A be the nn matrix with n=1000 and entries...Ch. 2.6 - Prob. 7CPCh. 2.6 - Prob. 8CPCh. 2.6 - Prob. 9CPCh. 2.6 - Prob. 10CPCh. 2.7 - Find the jacobian of the functions a....Ch. 2.7 - Use the Taylor expansion to find the linear...Ch. 2.7 - Sketch the two curves in the uv-plane, and find...Ch. 2.7 - Apply two steps of Newtons Method to the systems...Ch. 2.7 - Apply two steps of Broyden I to the systems in...Ch. 2.7 - Prob. 6ECh. 2.7 - Prove that (2.55) satisfies (2.53) and (2.54).Ch. 2.7 - Prove that (2.58) satisfies (2.56) and (2.57).Ch. 2.7 - Implement Newtons Method with appropriate starting...Ch. 2.7 - Use Newtons Method to find the three solutions of...Ch. 2.7 - Use Newtons Method to find the two solutions of...Ch. 2.7 - Apply Newtons Method to find both solutions of the...Ch. 2.7 - Use Multivariate Newtons Method to find the two...Ch. 2.7 - Prob. 6CPCh. 2.7 - Apply Broyden I with starting guesses x0=(1,1) and...Ch. 2.7 - Apply Broyden II with starting guesses (1, 1) and...Ch. 2.7 - Prob. 9CPCh. 2.7 - Apply Broyden Ito find the intersection point in...Ch. 2.7 - Apply Broyden II to find the sets of two...Ch. 2.7 - Apply Broyden II to find the intersection point in...
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