# iteration

1. ### Sets functions and iterations

I am new to algebra and help would be more than welcome to tell me if the process I have built is OK, and if my attempt to apply formula on two sets to create a new one is also OK. Context I have a database containing species records (e.g. 10 different species, with 100 rows by species ; in...
2. ### Convergence of an iteration

We have the following iteration: $x^{(k)}$ = G$x^{(k)}$ +b Spectral radius of A=10 and has eigenvalues > 5 Reason of not covergence is obvious. But how do we make it converge through either Jacobi, Gauss Siedel or SOR?
3. ### Iteration of double integrals

Tried solving it using substitution , hence u=x^2 du=2xdx not sure what to do next..
4. ### Matrix Iteration sequence constant value query

Hello all, currently stuck with this question and hopefully someone will point me in the right direction.
5. ### Jacobi and Gauss-Seidel Iteration question

One of my homework problems that I am stuck on. For the Matrix 1 2 -2 1 1 1 2 2 1 What is the spectrum for the Jacobi iteration matrix and the Gauss-Seidel iteration matrix. And are the methods convergent? Any information or help would be really appreciated.
6. ### Iteration

Hi, I've a big problem with an iterative exercice. Actually I don't know how to begin and it would be nice if someone could help me and say if I am wrong ... My problem is the following : $c_1, ..., c_n \in R^+_0$ and $A$ a matrix nxn such as : $a_{i,i}=2+c_i$ $a_{i,i+1}=a_{i,i-1}=-1$...
7. ### Solving an integral equation by iteration

Hello guys! I was given a Volterra integral equation y(x)=1/2*x^2+integral(0--->x) [t(t-x)y(t)]dt to solve using iteration. I have no idea how and where to start... The full problem goes as follows: Show that the solution y(x) of y''+xy=1, y(0)=y'(0)=1 also satisfies the integral equation...
8. ### linear iteration

A: (5 7) (-2 -4) eigenvalues are -2 and 3 eigenlines are y=-x and y=-(2/7)x Calculate the second and third points of the iteration sequence with recurrence relation Xn+1 = Axn (n = 0, 1, 2, . . .), for each of the following initial points. (i) (?1, 1) (ii) (1, 1) i have worked it already...
9. ### Common Iteration . Need help!

Someone maybe can explain me how use common iteration, when equation is lnx-(1/x)+M=0 ( I understand that the equation to be transformed in a form g(x)=x and i did it, x=(e^1/x)*(e^-M) but what's next...i'm not understand )
10. ### Reduce function value by iteration

Given certain function f(X) which is quadratic in X, in order to obtain its min, I set the gradient to 0 to obtain [tex ]\nabla f(X) = AX-b [/tex]  So, the solution to the following linear system AX=b  with the unknown X would give me the value that minimizes f(X). Since...
11. ### Common Iteration . Need help!

When i have the equation: lnx-1/x+M=0 How i can solve it, when need to use Common Iteration?
12. ### Order of Convergence of an Iteration

Please assist me how to find convergence/ order of convergence, or if it will converge or not. Which of the following iterations will converge to the indicated fixed point A (provided Xo is chosen sufficiently close to A). If the iteration does converge, give the order of convergence. For...
13. ### Numerical Analysis - Fixed Point Iteration

Assume that g is a continuously differentiable function and that the Fixed-Point Iteration g(x) = x has exactly three ?xed points, ?3, 1, and 2. Assume that g'(?3) = 2.4 and that FPI started suf?ciently near the ?xed point 2 converges to 2. Find g'(1). Guess F(x) = x^3 - 7x + 6 where -3...
14. ### How to you use iteration method

Use iteration method to solve the follwoing recurrence T(n) = { 1 if n =1 ------ -{ 4T(floor(n/2)) + n otherwise Show that an upper bound is correct forr n >= 1 and exact for n a power of 2. verify the upper bound with substitution method. I don't understand iteration method. It seems the...
15. ### Is there field of study dealing with function iteration?

I'm wondering if anyone knows of some kind of resource or field in mathematics that can explain some of the behaviour of iterated functions ie. applying a function to itself over and over again. For example, if f(x) = 2x, f iterated n times on x (written as f^n(x)) would be (2^n)x. I tried...
16. ### iteration group

greetings! this is a "can someone point me in the direction of this topic?" post... a current project uses an iterative procedure that produces a set of objects. a distinguishing feature of this set is that each object belongs to an equivalence class of objects. the equivalence relation is...
17. ### Using Iteration

so I need to guess a formula for the sequence Bk=B?k/2? + 1 for all integers k >= 2 and B1=1 So B2=2 B3=3 B4=3 B5=4 B6=4 B7=4 B8=4 B9=5 B10=5 ...... now Im having a hard time coming up with a formula, I tried Bn=1 + log of ?n? in base 2. However, this works for B2,B3,...... but not for B1. Any...
18. ### Polynomial iteration

Hello, given is a polynomial P(x)=x^2+4x+2. Find all solutions to the equationP^n(x)=0, where P^n(x)=\underbrace{ P(P(...P }_{n}(x)...)). I have managed to work out that the solutions are of the form \pm\sqrt[n+1]{2}-2, and then that...
19. ### Inverse Iteration -Problem

This is the question: Let Z_{n+1}=Z_n^2+2i and Z_0=0.5+0.2i find Z^{10} value and hence deduce the Z_n when n \to \infty
20. ### limit after fixed point iteration

In order to approximate to the number \bar{x}=ln3 we call the equation f(x)={e}^{x}-3=0. Show that the fixed point method {x}_{k+1}={x}_{k} - 0.1({e}^{{x}_{k}} - 3) , k=0,1,... converges to \bar{x} for every {x}_{o} \in [0,2]. Do 3 iterations, given that {x}_{o}=1, and find an estimation of...