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You are not logged in. #2 20121216 15:00:43
Re: IterationHi Still Learning; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #3 20121216 15:39:44
Re: IterationI am new to solving equation using iteration,so I dont know which equations can be solved using it,so please show me an example u like. #4 20121216 16:06:51
Re: IterationHi; There are many forms of iteration but we can do only one at at time so I pick this one. We need to get an x by itself on the LHS. Now we need an initial value for x. These can be attained from a plot of the function or in this case a guess. We will choose x1 = 1. For purposes of computation we will change that equation into a recurrence. Do you follow up to here? In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20121216 17:00:52
Re: IterationHi; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #7 20121216 17:12:42
Re: IterationDo i have to keep finding xn to infinity or there is a certain n? #8 20121216 17:19:21
Re: IterationNo, when you get convergence you stop. But it may take many iterations for that to occur. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #9 20121216 17:27:21
Re: IterationThank you it was very helpful,how does one solve system of equations using it?(just curious) #10 20121216 17:44:28
Re: IterationA system of equations is a little different. First you should see how the one we are doing is solved. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #12 20121216 19:42:26
Re: IterationVery good! If you try that one you will get a surprise. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #13 20121216 20:39:49
Re: Iterationhi Still Learning, on a graph (blue in my picture) and also the line shown red. You choose an initial guess (x1) and draw a vertical line until it meets the blue curve. This is at the point (x1,y1). Then you draw horizontally until you meet the red line. This is the point (y1,y1). But rename it (x2,x2) Now use x2 as the new value to try for x. Draw a vertical line until it meets the blue curve. This is the point (x2,y2) Draw horizontally from here to meet the red line at (y2,y2). Rename this (x3,x3). and so on. I have shown these movements as a green path. If this path spirals inwards towards a point, then the iteration is converging. Where the blue curve and the red line cross, is the solution. Sometimes the iterations do not move inwards towards the solution because the iteration isn't converging. So you have to find the right iterative equation. Surprisingly, all it depends on is the gradient of the blue curve at the point it crosses the red line. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #14 20121216 21:09:57
Re: IterationHi Bob and Still Learning;
If we start with an initial condition of 1 we get the following diagram called a cobweb. See fig 1. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #15 20121216 21:10:55
Re: IterationWow,that converges at 1.92318... And 0.54894...,why?and I have 2 other questions #16 20121216 21:18:41
Re: IterationIteration is more robust than the classical methods taught. It is a general method to solve any type of equation. You can use any initial condition but not all of them will converge. You would of course try to get a good initial guess for a simple system like this.
It does not converge it will keep being repelled by the root, going further and further away. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #17 20121216 23:52:15
Re: IterationYes,and about other answers,is there a iterative method for that? #18 20121216 23:58:21
Re: IterationUsually it is trial and error. To find other answers you try different initial conditions. For that cubic you would now try x1 = 1 + i maybe, since you know the other two answers are in the complex plane. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #19 20121217 01:25:58
Re: IterationThank you,but is there a rule for taking x to a side(as the second one you gave didn't solve) and you didnt write about system of linear equation.(again just curious) #20 20121217 09:59:14
Re: IterationX to a side? I do not understand what you are asking. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #21 20121217 10:18:42
Re: IterationI think he wants to know how to know which x to solve for to actually get the solutions that do not diverge... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #22 20121217 10:26:00
Re: IterationHi; A general rule here is to look for the largest coefficient and solve for that variable for each equation. Using that we get, We will use after 7 iterations, the roots are x = 2, y = 1.5, z = 4 / 3. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. 