1
vote
1answer
48 views

Find coefficients of polynomial that has zeros at certain points

Given a list of values z0, z1, ..., zn-1 (possibly with repetitions), show how to find the coefficients of a polynomial P(x) of degree-bound n + 1 that has zeros only at z0, z1, ..., zn-1 (possibly ...
5
votes
0answers
98 views

Generating Functions, Recursive Polynomials

At the CMFT international conference in Turkey (2009), the following open problem was given: Show that $$p_n(x):=\sum_{k=0}^n \frac{(n-k)^k}{k!}x^{n-k}$$ has only real simple zeros for every $n$. ...
3
votes
1answer
288 views

Recursive FFT java implementation

Given below is my java program for FFT. For the input {0,2,3,-1} its returns a false output in complex point representation. ...
8
votes
3answers
624 views

Karatsuba vs. Schönhage-Strassen for multiplication of polynomials

I am wondering how to most effectively multiply two polynomials with several 100's of coefficients, each coefficient having 1000-2000 decimal digits. I know Schönhage-Strassen begins to outperform ...
1
vote
1answer
352 views

Adding and Multiplying Polynomials Recursively

What theorem can be used to recursively multiply two polynomials together? Is there another theorem that uses recursion to add together two polynomials recursively? I'm looking for something that ...
6
votes
3answers
3k views

Using Horner's Method

I'm trying to evaluate a polynomial recursively using Horner's method. It's rather simple when I have every value of $x$ (like: $x+x^2+x^3...$), but what if I'm missing some of those? Example: ...
1
vote
2answers
553 views

Recursive method to evaluate a polynomial

I want to find a recursive way of evaluating any polynomial (I'm given the polynomial, and a value for x, and I need to replace the x in the polynomial with the value). The polynomial can be anything, ...