Recent content by gikiian

I am becoming clearer on this. Just correct me if I'm wrong. My new algorithm goes like: Substitute α=1 into the equation, and solve for λ - If λ∈(0,1), then the order of convergence is 1 - If λ=1, then the sequence converges sublinearly - If λ=0, then the order of convergence is greater than 1...

Got it! Quadratic convergence is a form of superlinear convergence. I still did not get this. Will we stop even if λ turns out to be ∞?

Why should I proceed? Wouldn't the sequence be shown to be superlinear already? Or can it be superlinear and quadratic at the same time?! Do you mind this correction?

Thanks a million! :!)

Are you saying that 10^{-2^{n}} should equal 10^{(-2)^{n}} instead of 10^{-(2^{n})}?

Homework Statement Show that the sequence {(p_{n})}^{∞}_{n=0}=10^{-2^{n}} converges quadratically to 0. Homework Equations \stackrel{limit}{_{n→∞}}\frac{|p_{n+1}-p|}{|p_{n}-p|^{α}}=λ where α is order of convergence; α=1 implies linear convergence, α=2 implies quadratic convergence, and so...

So my numerical analysis class requires me perform iterations involving huge expressions into my strictly NON-graphical scientific calculator. It often happens so that my current calculator (CASIO fx-911ES PLUS) does not allow me to feed in it a expression which goes beyond its input memory...

I have the ODE x''(t)+\frac{k}{m}x(t)=0. Given that the solution is of the form sin(ωt+ø), I plug this form into the original ODE and obtain ω=+\sqrt\frac{k}{m},-\sqrt\frac{k}{m}. And hence, I obtain two solutions of the ODE as follows: x_{1}(t)=Asin(\sqrt\frac{k}{m}t+ø)...

My undergrad senior-year Mechanical Vibrations book tells me that I should remember the notion that Asin(θ+ø) can also be represented in the form of Bsinθ+Ccosθ (and other linear combinations of sines and cosines), from high-school trigonometry class. However, I was never taught this in my...

Homework Statement As a part of Method of Frobenius, I am encountered with the following problems: Evaluate the following limits: Q1. \stackrel{limit}{_{x→0}}\frac{1-2x}{x} Q2. \stackrel{limit}{_{x→0}}\frac{x-1}{x} Q3. \stackrel{limit}{_{x→0}}\frac{1-2x}{x}+\frac{x-1}{x} In context of the...

Going to Trieste should be a rewarding experience as you get to work for betterment of the third-world countries (mostly Africa and South-Asia). On the other hand wherever you go, beauty will slowly fade away, and you'll have to live with the reality. In my humble opinion, beauty and...

As far as I can understand, ICTP collaborates with Elettra Synchrotron facility (http://www.elettra.trieste.it/) to fulfill its experimental needs.

Then I would strongly suggest ICTP (International Center for Theoretical Physics) in Trieste, Italy. Have a look around the website (www.ICTP.it).

Approach a good professor at Quaid-e-Azam University, Pakistan :) Some professors over there are competent internationally. I plan to get my masters degree in HEP from there.

THAT is what I wanted to see. Thank you very much Sir.