Iteration is the repetition of a process in order to generate an outcome. The sequence will approach some end point or end value. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration.
In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms.
I need insight on ##Q.2 (ii)## part only,
find mark scheme here;
How do we determine suitable equation, ##x=x...##?
ok, just looking at the solution, we shall have;
##2x^3+50 = x^3+100##
##x^3=50##
→##x##=##\sqrt[3]50##≡##3.68403## which is the value of ##α## ( convergent value as...
Hi. I would like to use a CAS to solve systems of nonlinear equations symbolically. The JavaScript library Nerdamer can solve single nonlinear equations symbolically shown here, and I would like to use that function iteratively to solve systems. For example, if I have a system of three equations...
Firstly, the cube root of 17 is 2.571281591 which is 2.57 to 3.s.f.
Initially, I thought about just approaching this problem using the Newton-Raphson Method when x0=2. In which case; x^3=17
x^3-17=0
Using the Newton-Raphson iterative formula xn+1=xr-f(xn)/f’(xn)
f(x)=x^3-17
f’(x)=3x^2...
On the following page on wikipedia:
https://en.wikipedia.org/wiki/Fixed-point_iteration
the section "Examples" has a second bullet point, where the author suggests ##q=0.85##, but how did they get this number? I tried googling everything and could not find out how ##q## is determined.
Hello to everyone!
I'm having a problem, banal in form, but perhaps complex in practical application.
Let's suppose we have 300 functions y = f (x) of random trend and we want to group these functions into 10 subgroups (each group consisting of 30 functions).
However, this grouping must not be...
I wouldn't be surprised if I've posted in the wrong section because in fact the reason for posting is to get help naming this problem. That being the first step to knowing where to look for a solution. Newbie to the forum so open to advice.
The problem: I have a complex histogram and a...
In OMP why the 'support' of the received signal is not found in one step, by selecting the $K$ maximum correlated columns of the sensing matrix $A$? where $K$ is the sparsity of the signal. Like in MATLAB
[val ind] = sort(A'*Y); %Y is received signal
signal_Support = ind(1:K)...
Hi i Have this equation:
T(n)=2T(n/2)+n^2
I understand for iterative substitution you need to find patterns so here's what i got:
2^2T(n/2^2)+n2/2+n^2
2^3T(n/2^3)+n2/2^2+n2/2+n^2
My question is what to do after you have found the pattern?
I want to understand which of these is computationally expensive (in the sense of computational time) which is more accurate. Also I want to understand which of these two problems (computations time + accuracy) of iterative methods are addressed by multi-grid methods?
QUESTION (2/2)
1) What are some alternatives to iterative design in control theory?
2) I have a certain plant transfer function PTF(s) that is higher order than two and non-unity numerator.
I want certain characteristics such as a certain damping ratio (zeta).
So I want approximate it as...
Homework Statement
Write an iterative function char* conversion(unsigned int num, int base),
that converts an integer num into any base (base <=10).
Homework EquationsThe Attempt at a Solution
How to transform the following recursive function conversion() into iterative:
#include <stdio.h>...
Hi,
Suppose there's an operation like the following:
x(t) = x(t-1) + rand(m..n)
with
x(t) = current value
x(t-1) = previous value
rand(m..n) = equally distributed random real number in the range of m and n
is there a way to estimate the value of x(t) after Y iteration without actually doing...
I'm under the impression that any implicit method for numerically solving ODE should be providing high stability in exchange for accuracy.
I'm trying to solve the differential equation:
dy/dx = -1000y + 3000 - 2000exp(-x) with intial conditions (0,0).
I still can't understand how come the...
Warning...this requires scripting and iteration, and is not theoretical -- it is a real problem I haven't been able to solve, but I'm sure someone here can... :-)
Data: each .csv file is a test recorded at a time interval of 7.5Hz and each file has 3 columns. The first column is time in...
Hey guys so I have this Calc 3 project and the end is throwing me for a loop. I've done the encoding part, and I've coded the standard iterative methods, but I don't see how the two correlate so I can use the iterative methods to decode a "y stream" with the inputs specified...
Homework Statement
I have to detect a pattern (11011) once this detected I put a 1 in my ouput Z to 1 to the 0 of the pattern.
Example :
11011001...
00100000...
Homework EquationsThe Attempt at a Solution
Homework Statement
f(x) is the function we want to minimize. Beyond being real-valued, there are no other conditions on it. (I'm surprised it's not at least continuous, but the book doesn't say that's a condition.) We choose the next x^k through the relation x^k = x^{k-1} + \alpha_{k}d^k. We...
Hello all, this is my first post here, so please excuse me if there are any mistakes or important information is left omitted. Now, my problem is quite intricate and specific so I will be thankful for any information I can get. Using Excel, I am looking to model the volume flow of air through...
I was wondering if there is a way of finding out the values of x1 for which an iterative formula converges.
Specifically, I am looking at the formula xn+1=0.25(xn3+1) and I am thinking about it in the context of finding roots of a function, although it would be great if there was a general way...
Homework Statement
Show that if given \mathbf{x}_0, and a matrix R with spectral radius \rho(R)\geq 1, there exist iterations of the form,
\mathbf{x}_{n+1}=R\mathbf{x}_0+\mathbf{c}
which do not converge.
The Attempt at a Solution
Let \mathbf{x}_0 be given, and let...
Homework Statement
In our fluid mechanics class we were taught that we could use the following equation to solve for the Darcy friction factor f:
To do this by hand:
1. Guess a value for 1/sqrt(F), guess 3
2. Get the right hand side result of the equation using 3
3. Use that result for the...
I haven’t really done much related to systems of linear equations for a couple years, so my memory is a bit faded. But, I was wondering if anyone could tell me what iterative method this is. I made it up a while ago to see if it would work, and have recently been coding it to see that it does...
Homework Statement
This isn't quite homework (though it's close), but I'm working on a quantum circuit and wish to implement an iterative method to find the square root of a number using elementary arithmetic operations (and without reciprocals). I've gotten most of it down, but the error...
I have got this integration:
\int_{-1}^{1}\frac{x^n}{(1+w^2-P^2-2wx+p^2x^2)^2}dx
And at the same time, I can provide several results when n is small.
For example:
when n=1, the result is
\frac{2w}{(1-P^2)(1-w^2)}
when n=2, the result is...
Maybe this question better belongs to programming section but I feel it has mathematics related doubt.
I want an intuition on how iterative and recursive approaches are different. Just look at the simple arithmetic progression. nth term is given as a + n.d. This can be derived using both...
Hi there,
I arrived at the solution for a electric potential problem for a semi-infinite cylinder (there was a potential distribution given for the boundary conditions but that's not important here).
http://i210.photobucket.com/albums/bb283/DidgeFrank/Cylinder_pot.jpg
The solution is...
Hello there,
Subdivision modeling is a tool which all 3D Modeling Softwares uses. Its about creating a low density mesh and computer creates higher density mesh until your box turn into a sphere.I found something about finding iterative fractal function of a 3D object for example Rodin...
Consider a partial differential equation describing the evolution of some function of a system which varies with time and space. A set of initial conditions and boundary are absolutely necessary for solving the equation. However, there are some numerical iterative methods for solving...
Hi,
As you can seeh here, according to wikipedia, the Runge-Kutta methods are iterative, but I don't see what is iterative about it. As I see it, starting from a certain value of x where you know y, you calculate y at x+h, then at x+2h, etc. Where is the iteration?
Homework Statement
(Ax = B)
A:
3.1410 -2.7180 1.4140 -1.7321
9.8690 2.7180 -7.3890 0.4280
2.2360 -2.4490 1.0000 -1.4140
31.0060 7.3890 -2.6450 0.1110
B:
3.316
0
3.141
1.414
The question in my Numerical Methods assignment asks to use the Jacobi Iterative method to solve the system...
Show that if (Spectral radius) ρ(M)≥1 then there are x0 and c such that the iteration xk+1 = Mxk+c fails to converge
I am very lost on how to solve this problem. All the literature I have been able to read up proves the converse of the statement. I am unable to crack this.
Show that if A is...
Homework Statement
The iterative method is used to find the approximate root of the equation x3 + x - 1000 = 0 in [9, 10]. What is the suitable iterative function?
Homework Equations
The Attempt at a Solution
How to find the iterative function and is there any conditions for one?
Thanks for...
Hey!
I have a project for a Circuits Simulation class which is basically the programming of a small spice software. So the program must be able to find dc solutions and do transient analysis. This means it can solve Ax = b for a large (think 10^6 X 10^6) sparse non-symmetric matrix A which is...
I have no programming experience and trying to get mathematica to do what I need it to do is frustrating. I have the following functions that I need to iterate. For notational purposes, k[t+1] is the value of K in the next period. w is a parameter.
k[t+1] = -x[t] - y[t] + w
x[t+1] =...
as a physicist , there are some integrals in several variables that are DIVERGENT
in order to regularize them i argue that for any integral in several variables
\int_{V} f(x,y,z)dV
you can always perform an interative integration (you integrate in variable 'x' for example keeping the...
_nx represents the nth iteration.
Homework Statement
Show that {_{n+2}}x = _nx + M^{-1}(b-A{_nx})
Homework Equations
{_{n+1}}x = _nx + M_1^{-1}(b-A{_nx})
{_{n+2}}x = {_{n+1}}x + M_2^{-1}(b-A{_{n+1}x})
M = M_1(M_1+M_2-A)^{-1}M_2
The Attempt at a Solution
I tried was...
Hello,
I have currently written a Fortran 77 simulation program that I need to display graphically for each timestep. So far it calls the system to have gnuplot open an include file that has the gnuplot script to plot from my data files and produce a jpeg. What I would like to do is have it...
Hi.
Anyway, learning this sort of makes me feel like I've chosen the wrong school for myself, but I'd like to try and see if I can understand this nevertheless.
See, I'm supposed to learn various numerical methods for solving systems of linear equations, like the Jacobi or the Gauss-Seidel...
Hi
i want the x -axis to go from 1 to 5, then plot the 2nd element of each pair, (so that they appear in a horizontal row ) for
lis = {{4, 2}, {1, 3}, {2, 5}}
I' ve been playing around with ListPlot and using it with Map[Last,
lis] but not getting what i want
my goal is to repeat...
Homework Statement
I have a physics problem, but the math part is where I am getting stuck. I have to use the iterative method, which I understand, but I can't seem to get the correct result. My problem is that I have to plug the value of x=1.9195 into an equation f1(x)=(x/10)(x+3). I get a...
Homework Statement
Suppose X ~ uniform (0,1) and the conditional distribution of Y given X = x is binomial (n, p=x), i.e. P(Y=y|X=x) = nCy x^{y} (1-x)^{n-y} for y = 0, 1,..., n. Homework Equations
FInd E(y) and the distribution of Y.The Attempt at a Solution
f(x) = \frac{1}{b-a} = \frac{1}{1-0}...
If one were to solve an iterative system, how would they do so. I'm studying them, and am wondering how to find fixed points?
For example, say I have x_{n+1}=x_{n}^{2} and was looking at fixed points how would I do so. I'm studying fixed points and attracting and repelling.
Hi all,
I'm looking for a an effective technique for solving a system of linear equations. It should always converge, unlike jacobi or gauss seidel etc. It has to be more efficient than ordinary gauss elimination or kramers rule for large matrices.
Thanks!
The other day I was playing with my calculator and noticed that
\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+...}}}} \approx 2
But, what is that kind of expression called? How does one justify that limit?
And, to what number exactly does converge, for example...
Homework Statement
First of all this is revision not homework =)
question is Xn+1 = Cuberoot ( 17.5-2xn)
answer lies between 2 and 3. i know the answer is 2.34 but what i don't get is why it is
xn+1 = equation, because when you put xn=2.34 into the equation you get 2.34 out...
http://img142.imageshack.us/img142/6899/asdaps7.jpg
I can't see how to do this at all, I can see how the methods come about easily enough, and of course find the root if needed and then show which converged faster. But I have nothing in my notes to hint me on how I can find which converges...
Hi,
I need to solve a multi-start iterative multivariate constrained nonlinear programming problem. But I can't seem to be find any package that will solve it for me. I have been wondering if anyone would be kind enough to tell me some packages that can solve the problem. (C/C++ packages...
Does a http://en.wikipedia.org/wiki/Tikhonov_regularization" solution for least squares have to be iteratively solved? Or is there a way to perform regularization via linear algebra, the way linear regression can be done by solving the (XTX)B=XTy normal equations?
I am having a devil of a time trying to successfully perform an iterative process for a particle’s energy in a finite well. The equation describing the energy for a finite well is transcendental thus requiring a graphical or numerical solution. Although, the graphical solution is straight...