Homework Answers
QUESTION 4 (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790,...
QUESTION 4 (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, F (3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system x2 + y = 9, 22 + y2 = 25, x, y > 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as...
Question 1 (10 marks) For a linear system Ax- b with 1 0 -1 A-1 2-1 2 -1 3 b=14 18 and compute by...
Please do question 5 for me. Thanks
Question 1 (10 marks) For a linear system Ax- b with 1 0 -1 A-1 2-1 2 -1 3 b=14 18 and compute by hand the first four iterations with the Jacobi method, using x()0 Hint: for the ease of calculation, keep to rational fractions rather than decimals Question 2 For the same linear system as in Question 1, compute by hand the first three iterations (10 marks) with the Gauss Seidel method,...
its a numerical analysis question QUESTION 4 (a) A natural cubic spline that fits the data...
its a numerical analysis question
QUESTION 4 (a) A natural cubic spline that fits the data given by (10) f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) z+ y = 9, 1² + y2 = 25, 2, y > 0. Perform one iteration of Newton's method to approximate the solution,...
QUESTION 4 (10) (a) A natural cubic spline that fits the data given by f(3.0) =...
QUESTION 4 (10) (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) 2+y=9, 22 + y2 = 25, 2,y> 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as the initial solution. [20]
Question 1 (10 marks) For a linear system Ax b with 1 0-1 A-1 2-1 2-13 and b4 18 compute by hand ...
Question 1 (10 marks) For a linear system Ax b with 1 0-1 A-1 2-1 2-13 and b4 18 compute by hand the first four iterations with the Jacobi method, usg0 Hint: for the ease of calculation, keep to rational fractions rather than decimals. (10 marks) Question 2 For the same linear svstem as in Question 1. compute by hand the first three iterations with the Gauss Seidel method, us0 Hint: for the ease of calculation, keep to rational fractions...
02. (8,2, 5) You are provided with a system of linear equations Ax - ye, where A R r ER2,yER2 and e e Ri. Let the s...
02. (8,2, 5) You are provided with a system of linear equations Ax - ye, where A R r ER2,yER2 and e e Ri. Let the spectral decomposition of A is given by V2/2 V2/2( containing 1 0 containing eigenvalues of A and V2/22/2 Lo 5 corresponding orthonormal eigenvectors a) Determine the best approximation of the unknow vector x, when the observerd vector y 181
02. (8,2, 5) You are provided with a system of linear equations Ax - ye,...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a)...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
Problem Two: (Based on Chapra, Problems 12.9 Consider the simultaneous nonlinear equations: 2-5-y y+i- 1. Plot...
Problem Two: (Based on Chapra, Problems 12.9 Consider the simultaneous nonlinear equations: 2-5-y y+i- 1. Plot the equations and identify the solution graphically. Page 1 of 2 2. Solve the system of equations using successive substitution, starting with the initial guess xo-y-1.5. Show two complete iterations. Evaluate &s for the second iteration. 3. Redo Part 2 using Newton-Raphson method . Automate the solutions in Parts 2 and 3 using MATLAB scripts 5. Solve the system of nonlinear equations by calling...
Please write code in MATLAB. HW12_4: Solve the system of nonlinear equations over the interval 0 st0.03 using ode45. Display the results on the same graph. Include a legend. x(0)-3, y(0)-2, z(0)-1 ax...
Please write code in MATLAB.
HW12_4: Solve the system of nonlinear equations over the interval 0 st0.03 using ode45. Display the results on the same graph. Include a legend. x(0)-3, y(0)-2, z(0)-1 ax dt dy dz
HW12_4: Solve the system of nonlinear equations over the interval 0 st0.03 using ode45. Display the results on the same graph. Include a legend. x(0)-3, y(0)-2, z(0)-1 ax dt dy dz
4. (20 pts) In this problem, we combine the Steepest Descent method with Newton's method for solv...
4. (20 pts) In this problem, we combine the Steepest Descent method with Newton's method for solving the following nonlinear system. en +en-13 = 0, 12-2113 = 4. Use the Steepest Descent method with initial approximation x0,0,0 three iterations x(1), x(2), and x(3) to find the first ·Use x(3) fron the above the result as the initial approximation for Newton's iteration. Use the stopping criteria X(k)-s(k 1) < tol = 10 9 Display the results for each iteration in the...
QUESTION 4 (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, F (3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system x2 + y = 9, 22 + y2 = 25, x, y > 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as...
Please do question 5 for me. Thanks
Question 1 (10 marks) For a linear system Ax- b with 1 0 -1 A-1 2-1 2 -1 3 b=14 18 and compute by hand the first four iterations with the Jacobi method, using x()0 Hint: for the ease of calculation, keep to rational fractions rather than decimals Question 2 For the same linear system as in Question 1, compute by hand the first three iterations (10 marks) with the Gauss Seidel method,...
its a numerical analysis question
QUESTION 4 (a) A natural cubic spline that fits the data given by (10) f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) z+ y = 9, 1² + y2 = 25, 2, y > 0. Perform one iteration of Newton's method to approximate the solution,...
QUESTION 4 (10) (a) A natural cubic spline that fits the data given by f(3.0) = -5.6790, f(3.1) = -3.6674, f(3.2) = -2.2178 is to be constructed. Write down explicitly the system of equations that need to be used to construct the required natural cubic spline. (b) Consider the nonlinear system (10) 2+y=9, 22 + y2 = 25, 2,y> 0. Perform one iteration of Newton's method to approximate the solution, starting with (2, 4) as the initial solution. [20]
Question 1 (10 marks) For a linear system Ax b with 1 0-1 A-1 2-1 2-13 and b4 18 compute by hand the first four iterations with the Jacobi method, usg0 Hint: for the ease of calculation, keep to rational fractions rather than decimals. (10 marks) Question 2 For the same linear svstem as in Question 1. compute by hand the first three iterations with the Gauss Seidel method, us0 Hint: for the ease of calculation, keep to rational fractions...
02. (8,2, 5) You are provided with a system of linear equations Ax - ye, where A R r ER2,yER2 and e e Ri. Let the spectral decomposition of A is given by V2/2 V2/2( containing 1 0 containing eigenvalues of A and V2/22/2 Lo 5 corresponding orthonormal eigenvectors a) Determine the best approximation of the unknow vector x, when the observerd vector y 181
02. (8,2, 5) You are provided with a system of linear equations Ax - ye,...
Let A be the matrix To 1 0] A= -4 4 0 1-2 0 1 (a) Find the eigenvalues and eigenvectors of A. (b) Find the algebraic multiplicity an, and the geometric multiplicity, g, of each eigenvalue. (c) For one of the eigenvalues you should have gi < az. (If not, redo the preceding parts!) Find a generalized eigenvector for this eigenvalue. (d) Verify that the eigenvectors and generalized eigenvectors are all linearly independent. (e) Find a fundamental set of...
Problem Two: (Based on Chapra, Problems 12.9 Consider the simultaneous nonlinear equations: 2-5-y y+i- 1. Plot the equations and identify the solution graphically. Page 1 of 2 2. Solve the system of equations using successive substitution, starting with the initial guess xo-y-1.5. Show two complete iterations. Evaluate &s for the second iteration. 3. Redo Part 2 using Newton-Raphson method . Automate the solutions in Parts 2 and 3 using MATLAB scripts 5. Solve the system of nonlinear equations by calling...
Please write code in MATLAB.
HW12_4: Solve the system of nonlinear equations over the interval 0 st0.03 using ode45. Display the results on the same graph. Include a legend. x(0)-3, y(0)-2, z(0)-1 ax dt dy dz
HW12_4: Solve the system of nonlinear equations over the interval 0 st0.03 using ode45. Display the results on the same graph. Include a legend. x(0)-3, y(0)-2, z(0)-1 ax dt dy dz
4. (20 pts) In this problem, we combine the Steepest Descent method with Newton's method for solving the following nonlinear system. en +en-13 = 0, 12-2113 = 4. Use the Steepest Descent method with initial approximation x0,0,0 three iterations x(1), x(2), and x(3) to find the first ·Use x(3) fron the above the result as the initial approximation for Newton's iteration. Use the stopping criteria X(k)-s(k 1) < tol = 10 9 Display the results for each iteration in the...
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