# fixed

1. ### Numerical analysis- fixed point iteration method

Q. Compute by the method of fixed point iteration a real root of the equation x^3 + x^2 - 1 =0 correct up to two decimal places. In the above problem if we take f(x)=0, then to solve it we can write f(x) in the form of x=g(x). Now g(x) can take three different forms. i) 1/sqrt(1+x) ii)...
2. ### For n fixed, demonstrate: sum(x^k, k = 0 .. n) = 1/(1-x)+o(x^n) when x->0

For n fixed, demonstrate: sum(x^k, k = 0 .. n) = 1/(1-x)+o(x^n) when x->0 where o is little o notation,
3. ### Finding roots of a function using (Fixed Point Iteration) Method

Hello, I want to get the roots of F(x) = -x^2 + 1.8x + 2.5 Using Fixed Point Iteration.... This is my attempt of solving: F(x) = x-G(x) = 0 x = x^2 - 0.8x - 2.5 I used initial x value of 0.8 since it satisfies the condition of convergence: G'(0.8) = 2x - 0.8 = 2*0.8 - 0.8 = 0.8 (<1)...
4. ### understanding Kakuktani’s fixed point theorm problem

I have an exercise as part of game theory that requires that I understand what compactness means. Kakuktani’s theorm as stated in my text says Let X be a compact convex subset of R^n and let f:X->X be a set-valued function for which all x in X the set f(x) is non-empty and convex AND the...
5. ### Fixed point iteration problem involving complex functions

in An AC circuit, a source of 1.0 + j0 pu is applied to a load consuming complex power S= 0.7+j0.8 pu through a line impedance (lumped) of 0.001 + j*0.4 pu . Find the complex voltage across the load. The formula for complex power is S = VI* where I is the current going into the load and where V...
6. ### Curve with normal passing through a fixed point

Hello! This time I need hint with this task: Let \alpha be a regular (arclength-parametrized) curve with nonzero curvature. Suppose all the normal lines to \alpha pass through a fixed point. What can you say about this curve?
7. ### fixed point method

if there is a function g(x)=sqrt(1+x^2) which satisfies all assumptions of fixed point method but still this iteration does not converge to any root why? i tried it by solving x(n+1)=g(x(n)) but i am getting x cancelled and left out eqn as 0=1 . what is the correct approach please help?
8. ### fixed point iteration

verify that the iteration x_{i+1}=x_{i}^{2}-2 will converge to solution epsilon=2 of the equation x^2-x-2=0 only of for some n0 all iterates xn with n>=n0 are equal to 2 ie only accidently in this do i have to prove or just verify if i have to prove then how? i know x(n+1)=g(x(n)) interval...
9. ### Optimal Control Problem: Constrained Optimzation with Fixed Endpoints

Hi. This is a problem I'm having hard time solving. The following "autonomous" optimization problem can also be solved using Calculus of Variations, but I prefer the Optimal Control approach: Determine x=x(t) solving max\int_{0}^{2}(x-\dot{x})dt subject to \dot{x}\in [0,1] and x(0)=0 and...
10. ### Straight Line through a Fixed Point

I am not able to solve this problem Two fixed straight line OX and OY are cut by a variable line in the points A and B respectively and P and Q are feet of perpendiculars drawn from A and B upon the lines OBY and OAX. Show that if AB pass through a fixed point, then PQ will also pass through a...
11. ### Fixed Point Iteration for f(x)=cos(x+(2)^(1/2))+x(x/2+(2)^(1/2))=0 on [-2,-1]?

I need a function g(x)=x such that the fixed point iteration converges to the root of the equation in the title (the root is -(2)^(1/2)). So |g'(x)|<1 on [-2,-1]. Thank you!
12. ### Existence of a solution to a system using fixed point theorem

Hi (,) denotes scalar product. I am trying to prove that the following system has a solution: $A$ is an nXn matrix and satisfies (Ax,x) < 0 for all non-zero vector x in R^n, b a vector in $R^n$, n finite, $x$ is the unknown vector, max(b-x,0) is the vector with components max(b^i-x^i,0) for i...
13. ### Fixed point iteration doubt

Hi! I was asked to find an approximation for a root of f(x)=2sin(x\pi)+x=0 on the interval [1, 2] using the fixed point iteration method, with p0=1. So, I got g(x)=x=(\arcsin(-x/2))/\pi However, that way I just get numbers very close to zero (which is a solution for the equation, but it's not...
14. ### Solving for a Constant Return to arrive at fixed end value

Hi I am working on putting together an excel formula that will allow me produce the correct constant return number which will allow me to reach a fixed end value. I have a fixed spending stream & beginning value and want to figure out what constant return will get me to my prespecified end...
15. ### Fixed Point

I need help this. Let (X,d) be a compact metric space and f:X goes to X be a function satisfying for every x,y element X x does not equal y implies d(f(x), f(y)) < d(x,y) also phi(x) = d(x,f(x)) is uniformly continuous for x element X Show that f has a fixed point i.e. there is an x0 element...
16. ### Joint Distribution, expected value correlation of a graphed triangle (Fixed)

Suppose X and Y are two independent random variables each distributed as $Uniform(0,1)$. 1) Find the joint distribution of X and Y. 2) Let U = \cos(2 \pi Y)\sqrt{-2\ln(X)} and $V = \sin(2\pi Y)\sqrt{-2\ln(X)}$. Find the joint distribution of U and V assuming that the transformation is...
17. ### fixed point problem in norm

set x(t)=1+∫2cos(s(f^2(s)))ds(from 0 to t) then check x(0)=1+∫2cos(s(f^2(s)))ds(from 0 to 0)=1 then the initial condition hold, by FTC, we have dx(t)/dt=2cos(tx^(t)), then solutions can be found as fixed points of the map but for secound part [0,T] i dont know how to begin can anyone help me ???
18. ### fixed production functions

There are two rms. The first fi rm has the production function: f(x; y) = min{2x; x + y}. The second firm has the production function f(x; y) = x + min{x; y}. (a) On the graph below, use red ink to sketch a couple of production isoquants for the first firm at output levels: y = 10, and...
19. ### Output shaping using a fixed input. I should know this :(

Hey guys.. So I'm working on a throttle management system for ebikes and I had a math questions for you fellas. Okay so imagine you have an input we will call this X. X is a value from 750-4095 Right now currently the X value is taken and Y is output... Currently Y is from 750-4095 Y=X WHAT...
20. ### Two way fixed effects regression

Anybody know how you would estimate gamma when it is multiplied by a interaction term(dummy variable x regressor) from a number of regressions?? Is there any info on calculations out there about calculating gamma....have really tried hard to find something and this is about the best i've come...