# Questions tagged [rootfinding]

For questions about the theory and process of finding the roots of a function (values where the function returns zero).

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

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 ...
162 views

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

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 ...
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1 vote
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### 1-dimensional nonlinear global minimization of kepler distance problem

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 ...
• 143
1 vote
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### Why is the definition of convergence different for root finding algorithms as compared to sequences?

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 $p\geq 1$ ...
1 vote
301 views

### Python libraries for larges scale optimization/rootfinding

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 ...
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### Complexity of recovering all roots of a polynomial

Given a polynomial of degree n and a list of putative roots $\{r_i\}_{i=1}^{n}$, we can verify that all the putative roots are indeed correct by $n$ applications of Horner's method. Hence verifying ...
• 2,155
44 views

### 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 $x$ ...
• 2,155
1 vote
44 views

### Solving the non-linear Hamiltonian using Scipy's root finding method

I am a complete novice to computational physics and am finding difficulty in implementing a code to iteratively solve for a $2\times2$ nonlinear Hamiltonian using Scipy's root solver. I can't seem to ...
86 views

### Sufficient condition for real roots of a polynomial of order $n>5$ with arbitrary real coefficients

I ask for help in solving the problem. I am developing an optimization program that selects the coefficients of a polynomial of order $n> 5$ so that all its zeros are just real numbers. And I ...
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### Solve Rational Equation for Root Music in MATLAB

I'm trying to estimate DOA in the Hybrid architecture using root music so I need to solve the attached equation to find the roots for the Root_Music equation in Matlab. Does anyone have an idea for ...
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1 vote
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### Solving general initial value problem $\mathbf{f}(\mathbf{x}, \mathbf{x'}, t)=\mathbf{0}$

The common form of initial value problem that can be solved using ODE integrator is $$\mathbf{x'}=\mathbf{g}(\mathbf{x}, t)$$ where $\mathbf{x'}=\partial\mathbf{x}/\partial t$. The initial ...
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### Pass forward intermediate results during iterative optimization

To investigate a counter-current flow heat exchanger while considering temperature dependent physical properties (such as specific heat $c_\textrm{p,i}$, heat conductivity $\lambda_\textrm{i}$, ...
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### Calculating the Jacobian for a function containing a derivative

I have the equation $F(t) = \phi u + \frac{1}{2}\frac{d^2u}{dt^2} + u^3$ and broadly speaking, my task is to calculate the $\phi$ and $u(t)$ such that $F(t) = 0$. I am testing out a new algorithm to ...
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1 vote
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### What is the use of arrayfun if a for loop is faster?

This may not be so much of a scientific computing question but more of a MATLAB question, if that is the case, please feel free to close or migrate the question. Root-finding problems are commonly ...
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### Providing Jacobian as LinearOperator in scipy.optimize.root

I asked this question a few days ago on stackoverflow, but I figure scicomp.stackexchange is probably a better place. Sorry for the double post. I want to solve a system of nonlinear equations using ...
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### Nonlinear root solving libraries which accept a Jacobian in band-storage

I'm in search for a library for solving large systems of non-linear equations, similar to MINPACK, but unlike MINPACK, can accept a Jacobian in band-storage. My Jacobian is sometimes not invertible, ...
2k views

### Solve non-linear equation in R

I need to solve the following equation for $x$ in [0, 1]. Assume $0<\alpha<1$ and $0<\lambda$. $$(1 - x)^{\alpha+1} - \lambda (x+1)^{\alpha+1} = -2\lambda (\alpha + 1) x^\alpha$$ Would very ...
1 vote
194 views

### 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<b<c) or (c<b<a) . Also, in the case I am ...
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