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You are not logged in. #1 20120411 16:08:58
The RRARRA: Riemann Rearrangement Algorithm we can usually generate a faster converging series with the transformation Notice that the series inside the curly brackets is itself an alternating series and the algorithm can be reapplied on it! 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. #2 20120411 16:14:35
Re: The RRAHi bobbym Last edited by anonimnystefy (20120411 16:17:18) 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 #3 20120411 16:21:51
Re: The RRAHi; 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. #4 20120411 16:31:20
Re: The RRACool! Again,thank you! 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 #5 20120411 16:44:38
Re: The RRAHi; 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 20120411 17:08:37
Re: The RRABut how many terms do we take for a 10 digits approximation? 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 #7 20120411 17:10:49
Re: The RRAYou can usually get the general term of the new alternating series 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. #8 20120411 17:18:01
Re: The RRAAha...Just what I thought. I just thought you had something better. 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 #9 20120411 17:25:55
Re: The RRAIt is enough to do the job, why do we need something else? 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. #10 20120411 17:30:03
Re: The RRADunno,but it seems that every time I try to reuse a method,you have a better one. 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 #11 20120411 17:37:03
Re: The RRAThere are always other methods. In numerical analysis there are thousands of methods. Experience helps in the choice of the correct one. Someday, you might read "Numerical Methods that Usually Work," by the great Forman S. Acton, my teacher. You will then learn that the greatest numerical mathematician is a chemist! 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 20120411 19:06:16
Re: The RRABut,for now we should use Leibniz? 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 #13 20120411 20:52:35
Re: The RRAAny alternating series that converges. What kind of example do you want? 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. #14 20120411 21:32:14
Re: The RRAAn easy one,for starters.Then maybe we can gradually go to some unusual series. 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 #15 20120411 21:34:21
Re: The RRAI am not following you. All that Leibniz does is bound the tail of an alternating series. Is that what you want to do? 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. #16 20120411 21:38:00
Re: The RRANo.Give me a simple alternating function to estimate to a certain number of digits and then lower the number of terms needed to get that estimate.I want to do the process you showed me. 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 #17 20120411 21:41:52
Re: The RRAHow many terms are needed to estimate the above sum with 11 correct digits. 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. #18 20120411 21:49:04
Re: The RRAWell,our first approximation using Leibniz rules says we need 38 terms.But we can do better than that! 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 #19 20120411 21:53:28
Re: The RRAHi; 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. #20 20120411 22:01:47
Re: The RRAI applied the RRA I got When I used Leibniz again it told me I needed 37 terms. Last edited by anonimnystefy (20120411 22:02:13) 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 #21 20120411 22:12:35
Re: The RRAThat is essentially what I got. You know what happened? 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. #22 20120411 22:16:00
Re: The RRAHi bobbym 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 #23 20120411 22:19:46
Re: The RRAFrom post #1
In this case it does not accelerate the convergence. 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. #24 20120411 22:20:23
Re: The RRAThen what? 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 #25 20120411 22:23:06
Re: The RRANumerical techniques have conditions on them. When you violate those conditions strange things can occur. Take the simplest and most familiar numerical technique, Newtons iteration. People think they understand it but they do not. It is a very temperamental beast like the RRA. 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. 