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...
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?
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...
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.