# What is Iterative: Definition and 58 Discussions

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.

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1. ### Solve the iterative problem below

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...
2. ### I Solving a System of Nonlinear Equations Symbolically

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...
3. ### Iterative root finding for the cube root of 17

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...
4. ### Understanding Iterative Derivatives of Log Functions

I have never used induction to justify the derivative to a function, so I don't know where to start. Does anyone have some tips?
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### I Error estimate for iterative convergence

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.
6. ### MHB Find the best function grouping with an iterative method

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...
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### A Summing simple histograms to recreate a more complex one

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...
8. ### Why OMP is iterative? Can we find the support in one step?

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)...
9. ### MHB What are the next steps after finding a pattern in iterative substitution?

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?
10. ### Comparing direct and iterative solution of linear equations

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?
11. ### Alternative Methods vs Iterative Design — Control Theory

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...
12. ### C: Recursive function into iterative

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>...
13. ### MHB Estimating result of an iterative operation involving random number

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...
14. ### Implicit iterative methods oscillating?

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...
15. ### Find Function/Transform for signal that minimizes CV of data

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...
16. ### Correlation between Iterative Methods and Convolution Codes

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...
17. ### Engineering Circuit Homework: Detect Pattern 11011

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
18. ### Iterative Minimization lemma proof

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...
19. ### Flow through Interconnected Tubes

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...
20. ### Values of x1 for which an iterative formula converges or diverges?

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...
21. ### Convergence of iterative method and spectral radius

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...
22. ### Archived Iterative method to solving the Colebrook-White equation

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...
23. ### What Iterative Method is This?

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...
24. ### Estimating the error of an iterative sequence

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...
25. ### An iterative quotient integration

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...
26. ### Recursive vs iterative approach

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...
27. ### Iterative procedure for potential distribution of a cylindrical problem?

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...
28. ### Fractal Question :Rodin Scupture to Low density Mesh to 2D to Iterative Function

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...
29. ### Iterative methods - causality violation?

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...
30. ### Wiki says that Runge-Kutta is iterative?

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?
31. ### The Jacobi Iterative method question

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...
32. ### Iterative methods to solve linear system of equations

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...
33. ### Finding the Iterative Function to Solve x3+x-1000=0

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...
34. ### Krylov subspace iterative method for large sparse matrix

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...
35. ### Mathematica Can Mathematica handle complex values in iterative mapping?

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] =...
36. ### Iterative integration in several variables

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...
37. ### Recurrence Relation for Iterative Solution of Ax=b

_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...
38. ### Fort 77 and gnuplot iterative output jpegs

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...
39. ### Iterative methods for solving systems of linear differential equations

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...
40. ### Mathematica Mathematica:Plotting an iterative list on one graph

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...
41. ### Solving Iterative Method Homework | Physics Problem Help

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...
42. ### Iterative expectation of continuous and discrete distributions

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}...
43. ### Iterative Systems of Difference Equations

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.
44. ### Iterative methods: system of linear equations

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!
45. ### Iterative square root? sqrt(2+sqrt(2+sqrt(

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...
46. ### Solving Iterative Formulas: Xn+1 Explained

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...
47. ### Iterative Methods: Faster Convergence Analysis

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...
48. ### Multi-start iterative multivariate constrained nonlinear programming

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...
49. ### Does least squares regularization have to be iterative?

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?
50. ### How do I calculate the initial alpha for an iterative process in a finite well?

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...