Use iteration to guess the formula:
dk = 3(dk-1) + 1 = 3(3(dk-2) + 1) + 1 = 3(3(3(dk-3) + 1) + 1) + 1 = 3^3 dk-3 + 3^2+3^1+3^0 = 3^k d0 + 3^k-1+...+3^1+3^0 = 3^k*3 + (3^k - 1)/2 = (3^k*6 + 3^k - 1)/2 = (7 3^k - 1)/2 so, dk is (7*3^k - 1)/2
Use iteration to guess the formula: di-3dk-i +1 withk2 1 do 3 di-3dk-i +1 withk2 1 do 3
Use iteration to guess an explicit formula for the
sequence...
Materials for Reference:
Homework Problems Solve the following problems 1. Use iteration to guess an explicit formula for the sequence. Use the formulas from summation formula.pdf to simplify your answers whenever possible. (Follow the solution of exercise set 57-problem #5, on page A-43) dk-4dk-1+3, for all integers k2 2,where d1-2 2. Use iteration to guess an explicit formula for the sequence. Use the formulas from summation formula.pdf to simplify your...
19. Use 1 iteration of Newton's method to approximate a solution to x-2xy y* 1.5 starting from the guess (0,1). Give the valueof xassociated with this iteration.
(4) Guess a formula for the sum (2n 1) (2n +1) 1.3 3.5 Prove your guess using induction
(4) Guess a formula for the sum (2n 1) (2n +1) 1.3 3.5 Prove your guess using induction
3) Use simple fixed-point iteration to locate the root of f(x) = 2 sin(x) - x Use an initial guess of Xo = 0.5 and iterate until Eg s 0.001%. Verify that the process is linearly convergent.
2. 3x 25」LX2 (a) Perform three iterations for the following iterative methods using initial guess x0. Compute relative residual for each iteration. (You can use a calculator) · Jacobi method » Gauss-Seidel method · SOR method with ω 1.2 (b) For each iterative method, express its iteration procedure in the following matrix form: In other words, determine B and c for (2).
2. 3x 25」LX2 (a) Perform three iterations for the following iterative methods using initial guess x0. Compute relative...
Guess formula and prove by induction
Σ(-1)-F2-1 1=1
code
in matlab
1. [2+1+1pt] Power Method and Inverse Iteration. (a) Implement the Power Method. Use your code to find an eigenvector of -2 1 4 A= 1 1 2 4 1 -2 starting with Xo = (1, 2, -1)7 and Xo = (1, 2, 1)7. Report the first 5 iterates for each of the two initial vectors. Then use MATLAB's eig(A) to examine the eigenvalues and eigenvectors of A. Where do the sequences converge to? Why do the limits...
Derive the formula for Newton-Raphson Iteration Method by truncating the Taylor series. Sorry for the wrong subject. I can't find chemical engineering in my subject list. Thanks for your help.
Determine the point of intersection between y-x3-2x+1 and y-x2 a) Use bisection to initialize the problem (at least two steps) b) Write out the iteration scheme for Newton's Method (define your own initial guess, and perform one iteration) c)Write out the iteration scheme for Secant Method (define your own initial guess, and perform one iteration)
Determine the point of intersection between y-x3-2x+1 and y-x2 a) Use bisection to initialize the problem (at least two steps) b) Write out the iteration...
I can't solve the problem(b)
I guess I have to use the fact that the pressure varies with depth,
but I can't apply that properly.