I am a newbie in the forum, and may not know certain editing tricks. For example, I am facing a number of problems, like;
-> Entering an equation with Subscripts - for example; x1, x2 ... etc. where 1 and 2 must appear as Subscripts.
-> Is there any way to enter fractions, like; (a + b + c) / d in proper factional format?
-> What does [Img] tag do?
Help will be appreciated.
This time, I came up with another confusion on the subject. Just over-viewing the subject, I found two entirely different (apparently, at least) formulae for the method. One is:
x1 = [a * f(b) - b*f(a)] / [f(b) - f(a)]; where a and b are two guess points.
The other is:
x = [xn - x(n-1)] / [f((xn) - f(xn-1)] * f(xn)
Are these two formulae actually the same or different for their use in different situations. Please help keeping in mind that I am just a toddler in this branch of mathematics.
I hope and wish bobbym is somewhere around.
Thanks in anticipation.
Yes Bobbym. Actually, I have shot both questions in dark - looking at some example problems. I calculated the Root geometrically, by drawing the curve and then tangents at f(xn) repeatedly (4 iterations only).
I still wonder:
(a)- Couldn't we find the root with classic algebra (Analytically)?
(b)- How to decide which method (Newton's, Bisection, Secant etc) should we use for a particular problem?
Your encouragement really helped me moving ahead. Thank you so much.
Thanks Bobbym. I got some hint. Some people, like myself, are not good at asking their questions well - I'll try to improve.
Is it one of the main reasons for using Numerical methods, called improved Approximation?
I have some idea on Single Precision & Double Precision Floating Point numbers; but still could not understand; why should we use Numerical methods for the problems; which can be solved with plain algebra (probably called Analytical methods?). A real life example; comparing the two methods may resolve my problem for ever.
I am afraid, you people may feel off for my too basic questions. I can request to bear with me just for a little while; until I start walking, from crawling, on the path of you geeks. Thanks.
This is very encouraging response, Bobbym. Here I have just copied the original question for solution:
Use Newton's Method to find the only real root of the equation
Use the Newton-Raphson method, with 3 as starting point, to find a fraction that is within 10^−8 of
I have copied the above questions from the question paper, given in an exam. It will be so nice to get my confusion cleared.
As an absolute novice in Numeric Analysis, I have another query - How the Numerical methods (Newton, Euler, Taylor, False Positioning etc.) help with higher Accuracy & Precision.
I mean, if I calculate an equation
Please pardon me for asking too basic questions. They may help me grasp the true essence of the subject.
Thanks in anticipation.
Sorry Bob, I did not see your reply before. Our syllabus, for this semester, is divided into three parts:
Part 1: General Concepts on Computer Science; which include Computer Architecture, Operating Systems and Data Structures etc.
Part 2: System Analysis & Design
Part 3: Numerical Methods. Complete solution of each problem is solved on papers, of course calculator is used just for basic operations.
Each part has a separate paper in the exam. We have already studied Programming in Pascal and C, in our previous semester. So Numerical Methods is an exclusive topic; not just a casual discussion.
Thanks for your attention, Agnishom.
I have searched the topic on the Net and found that these methods are taught to be solved manually in US and Europe, as well. On the Web, I found so many questions/answers (solutions) in PDF, for these methods, to help prepare for the college exams, in US and Europe. There is no mention of applying these methods on computers. Then what do they have to do with computer science?
I just want to straighten my perception on the subject; otherwise I will not be able to study it with confused mind.
Further help will be highly appreciated.
This is my first query and therefore may be too basic. Please, don't ignore it; because I am very much confused and seek help.
I have found a number of chapters on Numerical methods in our Computer Science studies. All the chapters and every problem teaches how to use Newton's method, Taylor Series, Bisection and Secant methods etc for solving questions MANUALLY; like we had been doing all the way till now.
There is no mention of using any of these methods using computers.
I assume, the subject is about using computational methods to solve certain problems; which can not be done manually. Have I wrong perception about Numerical methods? Why are these methods taught in Computer Science?
Would someone(s) be kind enough to clarify my confusion!
I have just joined the forum to share (rather just asking for solutions, at this stage :-) points on the Numerical Methods.
Actually, I have just taken Computer Science as an optional subject and found some quite daunting chapters on the subject. It forced me to join the wizards on this forum for some help.
I wish everyone very good time.