Let me rephrase, what I am having a problem with at this point is to relate the (B1,...,Bn-1) in my definition of P'(x) with the (C1,...,Cn-1) if I write P'(x) in the usual manner
P'(x)=sum(i=1,...,n-1){Ci*x^i}
Then obviously I can easily relate the Ci to your Ai.
I am not sure I understand what you are getting at.
I do not know if it helps or overlap with what you are saying but here is what I tried to do at this point: if P(x) is a polynomial of degree n, then its derivative P'(x) is a polynomial of degree n-1. Therefore, I have tried to...
Thank you for your suggestion. Sturm's theorem is something I could use. However, I am not sure how I can use it to find constraints on the coefficients that guarantee the monotonicity of the polynomial over [0,1].
What general constraints on the coefficients of a polynomial of degree n do I need to impose to guarantee that this polynomial is strictly increasing on [0,1]?
Hello everybody,
I am facing a Topology problem, and I hope you may be able to help me.
Let me try to describe my problem as clearly as I can: assume you have a set F of functions, such that any element f in F is a one-dimensional bounded and continuous function with common support S...