![1. Consider the following function F(x) x 2 where x = [x1 x2]T (d) Write a code to implement conjugate gradient method on thi](http://img.homeworklib.com/images/4fbf3c8f-a694-4d11-8f72-1d32222652b3.png?x-oss-process=image/resize,w_560)
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1. Consider the following function F(x) x 2 where x = [x1 x2]T (d) Write a code to implement conj...
*3. Consider a function, f(x,y) = x3 + 3(y-1)2 . Starting from an initial point, X0 = [1 1] T , perform 2 iterations of...
*3. Consider a function, f(x,y) = x3 + 3(y-1)2 . Starting from an initial point, X0 = [1 1] T , perform 2 iterations of conjugate gradient method (also known as Fletcher-Reeves method) to minimize the above function. Also, please check for convergence after each iteration.
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6?...
Consider the following function with a real variable, x: ?(?) = ?3 - 3?2 + 6? + 10 a. Write a Python function for the derivative of f(x) that takes x and returns the derivative of f(x). Take the derivative of f(x) analytically with respect to x before writing the function. b. Write a Python code that approximately finds the real root, x0, of f(x) such that f(x0)~0 using the Newton-Raphson method. The code is expected to get an initial...
from the previous two parts. E9.6 Consider the following quadratic function F(x) = *(3 21 -...
from the previous two parts. E9.6 Consider the following quadratic function F(x) = *(3 21 - + [a 4] i. Sketch the contour plot for F(x). Show all work. ii. Take one iteration of Newton's method from the initial guess X0 = 0 0 iii. In part (ii), did you reach the minimum of F(x)? Explain. E9.7 Consider the function F(x) = (1 + 4 + 2.680 - 12
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This function has its optimal solution atx"= (1,1) and f(1, 1) 10. Run t...
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This function has its optimal solution atx"= (1,1) and f(1, 1) 10. Run the k-th iterates of the Newton algorithm, and compute the descend the k-th iteration (dk). [5 marks] Resource Allocation prob
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This...
, to solve the equation set Given x=ly. I, L4」 f(x) Lf,(x)」"[x2-4-1」 , f(x)-0, with an initial...
, to solve the equation set Given x=ly. I, L4」 f(x) Lf,(x)」"[x2-4-1」 , f(x)-0, with an initial guess of x"-0, ie. , xi (0)-0 x2 (0)-0. a Using the Jacobian methods, determine the iteration unction, and the estimate value of x = x1 (b) Using the Newton-Raphson approach, determine the iteration function, and the estimate value of x2 after first two iterations, show the work. x=[x1,x2lT after first iteration. fa * Hint: the inverse ofa 2-dimension matrix: 1Ta b -b...
1. Consider a utility function u(x1, x2) = x1 + (x2)^a where a > 0. (a)...
1. Consider a utility function u(x1, x2) = x1 + (x2)^a where a > 0. (a) Show that if a < 1, then preferences are convex. (b) Show that if a = 1, then preferences have perfect substitutes form. (c) Show that if a > 1, then preferences are concave. (d) For each case, explain how you would solve for the optimal bundle.
2. Consider the following function: f (x1, x2) = x1 – 2V82 (a) Write down the...
2. Consider the following function: f (x1, x2) = x1 – 2V82 (a) Write down the Hessian matrix. (b) Is the function convex at the point (x1 = 1, X2 = 2)?
matlab 1. Given the system of equations 9 + x2 +x3 +x4 = 75 xi +8x2 x3x54 X1+X1 +7X3 + X4 = 43 xi+x2 +x6x434 Write a...
matlab
1. Given the system of equations 9 + x2 +x3 +x4 = 75 xi +8x2 x3x54 X1+X1 +7X3 + X4 = 43 xi+x2 +x6x434 Write a code to find the solution of linear equations using a) Gauss elimination method b) Gauss-Seidel iterative method c) Jacobi's iterative method d) Compare the number of iterations required for b) and c) to the exact solution Assume an initial guess of the solution as (X1, X2, X3, X4) = (0,0,0,0).
[4] Problem 4. Consider the following system [28' 12 3 x] after one iteration of Gauss-Seidel...
[4] Problem 4. Consider the following system [28' 12 3 x] after one iteration of Gauss-Seidel method using [x 13 Find the values of [x1 x]T-[0 0 0]" as the initial guess. X2 X2
Given initial conditions x1(0) = 1 and x2(0) = 0, determine solution components x1(t) and x2(t)....
Given initial conditions x1(0) = 1 and x2(0) = 0, determine
solution components x1(t) and x2(t).
7. Consider the following differential equation system for 11(t), 12(t), where x = (*1). x = (1 %)* (a) (7 points) Find the general solution.
from the previous two parts. E9.6 Consider the following quadratic function F(x) = *(3 21 - + [a 4] i. Sketch the contour plot for F(x). Show all work. ii. Take one iteration of Newton's method from the initial guess X0 = 0 0 iii. In part (ii), did you reach the minimum of F(x)? Explain. E9.7 Consider the function F(x) = (1 + 4 + 2.680 - 12
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This function has its optimal solution atx"= (1,1) and f(1, 1) 10. Run the k-th iterates of the Newton algorithm, and compute the descend the k-th iteration (dk). [5 marks] Resource Allocation prob
iu [5 marks]b ii)) Consider the function, f, as the followings,vRuǐ (x1, x2)-5xỈ + x-. + 4x1 x2-14x1-6x2 + 20 ( !0% x») This...
, to solve the equation set Given x=ly. I, L4」 f(x) Lf,(x)」"[x2-4-1」 , f(x)-0, with an initial guess of x"-0, ie. , xi (0)-0 x2 (0)-0. a Using the Jacobian methods, determine the iteration unction, and the estimate value of x = x1 (b) Using the Newton-Raphson approach, determine the iteration function, and the estimate value of x2 after first two iterations, show the work. x=[x1,x2lT after first iteration. fa * Hint: the inverse ofa 2-dimension matrix: 1Ta b -b...
2. Consider the following function: f (x1, x2) = x1 – 2V82 (a) Write down the Hessian matrix. (b) Is the function convex at the point (x1 = 1, X2 = 2)?
matlab
1. Given the system of equations 9 + x2 +x3 +x4 = 75 xi +8x2 x3x54 X1+X1 +7X3 + X4 = 43 xi+x2 +x6x434 Write a code to find the solution of linear equations using a) Gauss elimination method b) Gauss-Seidel iterative method c) Jacobi's iterative method d) Compare the number of iterations required for b) and c) to the exact solution Assume an initial guess of the solution as (X1, X2, X3, X4) = (0,0,0,0).
[4] Problem 4. Consider the following system [28' 12 3 x] after one iteration of Gauss-Seidel method using [x 13 Find the values of [x1 x]T-[0 0 0]" as the initial guess. X2 X2
Given initial conditions x1(0) = 1 and x2(0) = 0, determine
solution components x1(t) and x2(t).
7. Consider the following differential equation system for 11(t), 12(t), where x = (*1). x = (1 %)* (a) (7 points) Find the general solution.
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