Recent content by hsong9

I need to keep track of the size of the matrix myself. This means I can't use "size" function. Is it possible? For example, A is a 5 x 5 matrix. I need to create a vector x=[0,0,0,0,0]. It should be just x = zeros(size(A,1),1); %or length(A) but I need to check the size of A matrix...

Thanks! So, to minimize S, set partial derivative for a and b equals to zero. right? Thanks again.

Thanks! the relationship is y = ax + b/x. Thus, S = Sigma ( y_k - (ax + b/x))^2, right? and that's it?

Homework Statement Suppose a set of N data points {(xk,yk)}Nk=1 appears to satisfy the relationship for some constants a and b. Find the least squares approximations for a and b. Homework Equations The Attempt at a Solution I really have no idea about this problem.

Hi, Could someone please show me how to solve the following simple problem using the Runge-Kutta (RK4) integration method? (tw')' + tw = 0 with w(0) = 1, w'(0) = 0 on the interval [0,1] by introducing the new variable v=tw' and considering the resulting first order differential system...

I got the answer. It's only 4-5lines. Thanks!

I think f(x) = x^(5/4) is fine as your hint. And also f(x) is convex as condition of x_{i} --> positive real numbers. Right?

You mean I have to make some convex function and then apply into the inequality. Finally, I will get the answer. Right? hmm, If so, I will think about the function.

Thanks for your hints, but I am not sure yet. If I have x^4 = y and x^5 = y^(5/4), then I get the inequality which is just the same with the problem. how do I get the inequality of Jensen? (without logarithms?) Thanks

I know Jensen's inequality, but I am not sure how it will work for my question. Can you give me some hints? Thanks

Homework Statement Let X1,X2,...,Xn be positive real numbers. Show that ((x15+...+xn5 )/ n)1/5 >= ((x14+...+xn4 )/ n)1/4 Homework Equations The Attempt at a Solution I have tried by taking logarithms. Is it right approach? Or.. It can be applied to AM-GM-HM inequality? how?

Thanks!

Sorry, my writing was confused. I konw Jensen’s inequality. Suppose that f(x) is a convex function defined on a convex subset C of Rn. If a1,...,ak are nonnegative numbers with sum 1 and if x(1),...,x(k) are points of C, then f(∑aix(i)) <= ∑aif((i)). f(x) = log(1+ex)...

Thanks, so.. f(x) = (1+ex) (1+x1)1/n...(1+xn)1/n = (1+elnxn)1/n ==> f(x) Thus, Σ((1/n)log(1+elnxi)) = Sigma (f(x)*(1/n)) Also, log (1+ (ex1...xn)1/n = log (1 + eln Σxi(1/n)) Therefore, Σ(f(x)*(1/n)) >= f(Σ(1/n)*xi) as required. right? I am not sure log (1 + eln...

Homework Statement verify that f(x) = log(1+ex) is convex and use this to show that (1+x1)1/n(1+x2)1/n..(1+xn)1/n >= 1 + (x1x2...xn)1/n where x1,x2,...xn are positive real numbers. Homework Equations The Attempt at a Solution I know f(x) is convex b/c f''(x) is always positive...