For questions about the theory and process of finding the roots of a function (values where the function returns zero).
Questions tagged [rootfinding]
55 questions
7
votes
1 answer
Fast computation of the zeros of a trigonometric polynomial
I am wondering what is the fastest way to compute the zeroes of the trigonometric polynomial
$$
T(x) = \sum_{i=1}^La_i\sin\big(2\pi(a_i x) - \phi_i \big), \\
a_i \in \mathbb{N}, \\
\phi_i \in \left[-\pi,\pi\right[, \\
x \in …
Arrigo
- 301
- 1
- 5
5
votes
0 answers
Roots of transcendental equation involving bessel functions
I need an efficient way to numerically find the first $n$ positive roots $\lambda_n$ of the transcendental equation
$$ \dfrac{J_0 (\lambda_n r) Y_1 (\lambda_n) - J_1 (\lambda_n) Y_0 (\lambda_n r)}{J_0 (\lambda_n r) Y_0 (\lambda_n) - J_0 (\lambda_n)…
Luis Costa
- 181
- 3
1
vote
1 answer
Help understanding Brent's root finding method
Help me understand a part of Brent's root finding algorithm. In a typical iteration we have samples (a,fa), (b,fb), (c,fc) all real with (a
Ted Ersek
- 111
- 3
0
votes
3 answers
finding all zeros of a continuous function
Let $f: \Bbb R \to \Bbb R$ be continuous. What are efficient algorithms to finding all the zeros in an interval $[a, b]$? I am actually only interested in the smallest zero in that interval, if there's an algorithm that can provide me with just…
Joe Shmo
- 121
- 5
0
votes
0 answers
Expected residual at double root
In a generic rootfinding problem $f(x) = 0$, we assume that the probability that the root $x$ is a floating point representable is zero. Hence, the best floating point approximation $\hat{x}$ to $x$ gives $f(\hat{x}) = f(x(1+\delta)) = x\delta f'(x)…
user14717
- 2,155
- 13
- 14