Questions tagged [rootfinding]

Question 1

I am working on evaluating the integral: $ I(\vec{r}) = \int f(k) e^{i\vec{k} \cdot \vec{r}} d\vec{k}, $ for a system with a tight-binding dispersion relation given by: $ \epsilon_k = -2t \left[\cos(...

Question 2

Tried to solve this equation for a week with multiple initial guesses using Muller method ( In scilab ) . But no success as of now. Tested the algorithm by finding root for various different complex ...

Question 3

I need to implement a root-searching algorithm for a function, that can possibly have some divergence points (DPs), or non-removable singular points, e.g. ...

Question 4

I have a differentiable function $\mathbb{R}^n \to \mathbb{R} $ of several variables $f(x_1,\ldots,x_n)$, whose form I can write down and compute derivatives of. Typically $n = 8$. The function is ...

Question 5

I have a smooth function $F: \mathbb{R}^n \to \mathbb{R}^{n-1}$ and points $x_0, y_0$ with $F(x_0) = y_0$. For theoretical reasons, I know that $y_0$ is a regular value of $F$, which means that the ...

Question 6

I want to solve the problem to determine the next intersection of a Keplerian orbit with the Sphere of Influence of a celestial body to find the next intersection within one future period of the ...

Question 7

The definition of convergence for root finding algorithms is given in a few sources as: A sequence ${x^k}$ generated by a numerical method is said to converge to the root $\alpha$ with order $p\geq 1$ ...

Question 8

I have been dealing with the standard libraries of scipy.optimize for rootfinding and optimization problems, but the problems i want to solve are very large, which makes the standard solvers run out ...

Question 9

I've made a previous question here and also in SO wondering why only the fsolve solver converges for the simple one dimensional unsteady conduction problem $$ \frac{\partial T}{\partial t} = \alpha \...

Question 10

I'm running a test problem to set up larger problems. Solving the simple unsteady heat equation via finite differences: $$ \frac{\partial T}{\partial t} = \alpha \frac{\partial^2T}{\partial x^2}$$ $\...

Question 11

I'm using a numeric root-finder to find $k$ satisfying $\|A^k x\|=c$ where $A$ is a symmetric $d\times d$ diagonal + rank-1 matrix. How to compute $A^k x$ efficiently? For integer $k$, I can get the ...

Question 12

I have coded a simple program for a root finding problem using Halley's method. Here is the code: ...

Question 13

Consider the following expression: $$f(t) = B+\sum_{k=1}^{N} A_k\cos(\omega_kt)$$ where $A$ and $B$ are known. the frequencies are also known but are not multiples of a fundamental frequency. However, ...

Question 14

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'...

Question 15

I was working on a problem recently (calculating all flows in a network given input and output flows, basically what Hardy-Cross tries to achieve) which can be formulated as a well-determined system ...

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Questions tagged [rootfinding]

How to Integrate in Energy Domain for a Tight-Binding System?

Numerical solution to 4 layer waveguide

Determine divergence points/singularities in root search of a non-continuous function

Algorithm to find local minima of function which is unbounded from below

Is there a software package that can compute the 1-dimensional preimage of a point?

1-dimensional nonlinear global minimization of kepler distance problem

Why is the definition of convergence different for root finding algorithms as compared to sequences?

Python libraries for larges scale optimization/rootfinding

Scipy.root not converging even when provided with initial guesses very close to solution

Why is this scipy.root code not converging?

Computing powers of diagonal + rank-1 matrix?

Dynamic tolerance in a conditional loop to obtain maximum precision allowed by machine floating point numbers

Summation of trigonometric functions results in error with finite precision

finding all zeros of a continuous function

Splitting system of equations into linear and nonlinear part and solving separately

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