Homework Answers
![Given that f/) - 24,4 + 4x 2 8 2 Ho la go-offer) - (if d=-Hog -- go = (id We know that L = -(good (drado --[814][14 5f88-8 +1](http://img.homeworklib.com/questions/b2cf2d00-0fec-11eb-843e-f7f8eaa38d78.png?x-oss-process=image/resize,w_560)
![-0.146 ogs 03523 -0783 0.85302 0.3523-12 0.552372 0. RIG826 0 85302 d=-H,9 = 0.352372/5.3358 -IS6567] 0.2768 0352372 = 10](http://img.homeworklib.com/questions/b4d94d80-0fec-11eb-9a19-a78427437b04.png?x-oss-process=image/resize,w_560)
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Numerical Analysis: Apply the BFGS Method to minimize the function f(x) = x12 - 2x1x2 +...
course: Numerical analysis 3. Consider Rosenbrock's banane valley function f(x,y) = (x-1) + 100 (4-x², henceforth...
course: Numerical analysis
3. Consider Rosenbrock's banane valley function f(x,y) = (x-1) + 100 (4-x², henceforth called the banana function. (a) Compute the gradient I f(x,y) of the banana function (6) Using (xo, Yo) = (-1.2, 1.0) as an initial point perform one iteration of the method of steepest, descent to explicitly find (X,Y). Refer to attached graph of level curves of the banana function. (XY)(-1.0301067/27..., 1.069344-19888...) and f(X,Y) S 401280972736-n, (c) Using (xoxo) = (-1-2, 1.0) as an initial...
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is...
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as Ok = argmin f(x“ – av f(x)). a20 (a) (3 points) Consider the objective function f(x):= *xAx- Ax - c^x + d. where A e RrXnCER”, d E R are given. Assume that A is symmetric positive definite and, at xk, f(x) = 0....
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is...
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as Ok = argmin f(x“ – av f(x)). a20 (a) (3 points) Consider the objective function f(x):= *xAx- Ax - c^x + d. where A e RrXnCER”, d E R are given. Assume that A is symmetric positive definite and, at xk, f(x) = 0....
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is...
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as Ok = argmin f(x“ – av f(x)). a20 (a) (3 points) Consider the objective function f(x):= *xAx- Ax - c^x + d. where A e RrXnCER”, d E R are given. Assume that A is symmetric positive definite and, at xk, f(x) = 0....
Use the method of Lagrange multipliers to minimize the function subject to the given constraints. f(x,y)...
Use the method of Lagrange multipliers to minimize the function subject to the given constraints. f(x,y) = xy where x2 + 4y2 = 4 and x 20 Find the coordinates of the point and the functional value at that point. (Give your answers exactly.) X = y = f(x,y) =
3. a) Short questions (Please briefly jiustify your answers in each case to receive full credits)...
3. a) Short questions (Please briefly jiustify your answers in each case to receive full credits) i) If we wish to minimize a function, fx.v)- 2x245x2+10, using Univariate Search method, how many searches will it take to reach the minimum and why? ii) Starting from an initial guess, Xo the minimization of the following function using Newton-Raphson method fails to work. Please explain why. f(X)-0.5x2 +2x1x2-(1/3)x +50 Note: N-R method: X- X1 - [ H(X 1)] 'Af(X), where H is...
The steepest descent method for minimize f(x) is the gradient descent method using exact line search,...
The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as ak = argmin f(xk – aVf(xk)). a>0 (a) (3 points) Consider the objective function f(x): = *Ax – cx+d, where A e Rnxn, CER”, d E R are given. Assume that A is symmetric positive definite and, at xk, Vf(xk) + 0. Give a formula of ak in terms xk, A, c,...
numerical analysis 1 f (x + 2h) f"(x) = 2f (x + h) + f (x)...
numerical analysis
1 f (x + 2h) f"(x) = 2f (x + h) + f (x) 12 Forward difference II f(x - 2h) f"() = 25(x - hr) 12 method Backward method difference f'(x) = -f(+ 2) + 4(x +h)- 36) 2h Forward difference method Which ones are correct? a) I, II b) Only 11 a d) Only 1 e> I, II, III
Numerical Analysis Q5: Using Newton's method, Find the root of x3 = 6 x - 4...
Numerical Analysis
Q5: Using Newton's method, Find the root of x3 = 6 x - 4 corrected to 3 decimal places. Xo = 1.0 Q6: Use Gauss Elimination method to solve the following system of equations: 2x1 + 6x2 + 13x3 = 4 2x2 + x1 + 4x3 = 3 3x1 + 14x3 + 8x2 = 13
C++ Euler's method is a numerical method for generating a table of values (xi , yi)...
C++ Euler's method is a numerical method for generating a table of values (xi , yi) that approximate the solution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The first entry in the table is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) is obtained using the formula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is...
course: Numerical analysis
3. Consider Rosenbrock's banane valley function f(x,y) = (x-1) + 100 (4-x², henceforth called the banana function. (a) Compute the gradient I f(x,y) of the banana function (6) Using (xo, Yo) = (-1.2, 1.0) as an initial point perform one iteration of the method of steepest, descent to explicitly find (X,Y). Refer to attached graph of level curves of the banana function. (XY)(-1.0301067/27..., 1.069344-19888...) and f(X,Y) S 401280972736-n, (c) Using (xoxo) = (-1-2, 1.0) as an initial...
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as Ok = argmin f(x“ – av f(x)). a20 (a) (3 points) Consider the objective function f(x):= *xAx- Ax - c^x + d. where A e RrXnCER”, d E R are given. Assume that A is symmetric positive definite and, at xk, f(x) = 0....
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as Ok = argmin f(x“ – av f(x)). a20 (a) (3 points) Consider the objective function f(x):= *xAx- Ax - c^x + d. where A e RrXnCER”, d E R are given. Assume that A is symmetric positive definite and, at xk, f(x) = 0....
2. Steepest descent for unconstrained quadratic function minimization The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as Ok = argmin f(x“ – av f(x)). a20 (a) (3 points) Consider the objective function f(x):= *xAx- Ax - c^x + d. where A e RrXnCER”, d E R are given. Assume that A is symmetric positive definite and, at xk, f(x) = 0....
Use the method of Lagrange multipliers to minimize the function subject to the given constraints. f(x,y) = xy where x2 + 4y2 = 4 and x 20 Find the coordinates of the point and the functional value at that point. (Give your answers exactly.) X = y = f(x,y) =
3. a) Short questions (Please briefly jiustify your answers in each case to receive full credits) i) If we wish to minimize a function, fx.v)- 2x245x2+10, using Univariate Search method, how many searches will it take to reach the minimum and why? ii) Starting from an initial guess, Xo the minimization of the following function using Newton-Raphson method fails to work. Please explain why. f(X)-0.5x2 +2x1x2-(1/3)x +50 Note: N-R method: X- X1 - [ H(X 1)] 'Af(X), where H is...
The steepest descent method for minimize f(x) is the gradient descent method using exact line search, that is, the step size of the kth iteration is chosen as ak = argmin f(xk – aVf(xk)). a>0 (a) (3 points) Consider the objective function f(x): = *Ax – cx+d, where A e Rnxn, CER”, d E R are given. Assume that A is symmetric positive definite and, at xk, Vf(xk) + 0. Give a formula of ak in terms xk, A, c,...
numerical analysis
1 f (x + 2h) f"(x) = 2f (x + h) + f (x) 12 Forward difference II f(x - 2h) f"() = 25(x - hr) 12 method Backward method difference f'(x) = -f(+ 2) + 4(x +h)- 36) 2h Forward difference method Which ones are correct? a) I, II b) Only 11 a d) Only 1 e> I, II, III
Numerical Analysis
Q5: Using Newton's method, Find the root of x3 = 6 x - 4 corrected to 3 decimal places. Xo = 1.0 Q6: Use Gauss Elimination method to solve the following system of equations: 2x1 + 6x2 + 13x3 = 4 2x2 + x1 + 4x3 = 3 3x1 + 14x3 + 8x2 = 13
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