# NLsolve false convergence
**URL:** https://discourse.julialang.org/t/nlsolve-false-convergence/50922
**Category:** New to Julia
**Tags:** numerics, nlsolve
**Created:** [November 29, 2020, 12:08am UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922 "2020-11-29T00:08:27Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@Maria95](https://discourse.julialang.org/u/Maria95)
#### Post date: [November 29, 2020, 12:08am UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922/1 "2020-11-29T00:08:27Z")
Hi, I am a new user of Julia and this may sound like a basic question. I am trying to use NLsolve to find a solution to an equation of the form:
f(x)= ∑a0+a1 \*1/(1+x)^(b[1])+a2 \*1/(1+x)^(b[2])+ a3 \*1/(1+x)^(b[3])+⋯
By a substitution of variable y = 1/(1+x), this can also be written as:
f(y)= ∑a0+a1 \*y^(b[1])+a2 \*y^(b[2])+ a3 \*y^(b[3])+⋯
where a and b are constants
I set the show\_trace to false, but it still displays the log. I just want it to return the value for the Zero if the algorithm has converged. Upon some experiments, I discovered that the algorithm sometime incorrectly display the status as converged when using the Anderson method. On some sets of data I also got Domain error when using the Anderson’s method (the form f(y) is more likely to give this error).
In short, I need help with:
- Only to get the result of the variable (x in the code) if the algorithm has converged without displaying the trace. I don’t want the program to throw an exception like Domain error, but something like #Num if it gets into numerical difficulties.
- What’s wrong with my code that the algorithm falsely claims convergence in some instances or I am misinterpreting the results?
```julia
using NLsolve
function my_func(x,a,b)
A= Vector{Float64}(undef,length(b))
for i in eachindex(b)
A[i] = 1/(1+x[1])^b[i]
end
return a'*A
end
function my_deriv(x,a,b)
A= Vector{Float64}(undef,length(b))
B= Vector{Float64}(undef,length(b))
for i in eachindex(b)
A[i] = 1/(1+x[1])^(b[i]-1)
B[i] = -b[i]*a[i]
end
return B'*A
end
function f!(F, x)
F[1] = my_func(x,a,b)
end
function j!(J, x)
J[1,1] = my_deriv(x,a,b)
end
a=[-10,1,1,11]
b=[0,1,2,3]
nlsolve(f!, j!, [0.0];method =:anderson,show_trace=false) #The convergence flag is displayed as true though the Zero result is incorrect * Zero: [-4.798376404676865e23]
nlsolve(f!, j!, [0.0];method =:newton,show_trace=false) # Gives the right answer
```
---
### Author:  [@AndiMD](https://discourse.julialang.org/u/AndiMD)
#### Post date: [November 29, 2020, 11:55pm UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922/2 "2020-11-29T23:55:58Z")
Hi, unfortunately `nlsolve` claims it is converged when the iterations do not make progress (and xtol==0).Thus, you should also (or only) check `f_converged`:
```julia
res = nlsolve(f!, j!, [0.0];method =:anderson,show_trace=false,beta=1.0,ftol=1E-10,xtol=1E-12)
all_converged(res) = res.x_converged && res.f_converged
@show all_converged(res)
```
The Anderson method stability depends on its parameters. Setting `beta=0.1` seems to make it work. The Anderson method is probably not the best choice for your problem.
---
### Author:  [@Maria95](https://discourse.julialang.org/u/Maria95)
#### Post date: [December 1, 2020, 2:29pm UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922/3 "2020-12-01T14:29:59Z")
That’s fabulous. Thank you
---
### Author:  [@ctkelley](https://discourse.julialang.org/u/ctkelley)
#### Post date: [December 1, 2020, 2:38pm UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922/4 "2020-12-01T14:38:43Z")
Terminating any iteration on small steps is risky in most cases. Consider
\sum\_{n=1}^\infty 1/n
This series diverges. If you evaluate the sum numerically in order, starting with n=1, the sum will stagnate once 1/n is small enough for rounding effects to take over. That stagnation does not imply convergence.
Terminating a nonlinear solver on small residual norms is better. The quality of the residual norm as a surrogate for error depends on the conditioning of the Jacobian.
---
### Author:  [@Maria95](https://discourse.julialang.org/u/Maria95)
#### Post date: [December 1, 2020, 3:48pm UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922/5 "2020-12-01T15:48:07Z")
Thank you.
Do you mean something like this?
```julia
convergence_criteria(res) = res.residual_norm <= 1.0e-10
x _res = Float64
if convergence_criteria(res) == true
x_res = res.zero[1]
else x_res = "Error"
end
```
---
### Author:  [@ctkelley](https://discourse.julialang.org/u/ctkelley)
#### Post date: [December 1, 2020, 4:21pm UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922/6 "2020-12-01T16:21:08Z")
I’m not clear on what your code is doing. In any case, if you are solving a system of nonlinear equations
F(x) = 0
Then you’d terminate the iteration when \| F(x\_n) \| \< \tau\_r \| F(x\_0) \| + \tau\_a. Here \tau\_r and \tau\_a are relative and absolute error tolerances. This is documented in
```julia
author="C. T. Kelley",
title="{Iterative Methods for Linear and Nonlinear Equations}",
publisher="SIAM",
address="Philadelphia",
year=1995,
series="Frontiers in Applied Mathematics",
number=16
```
and
> **[GitHub - ctkelley/NotebookSIAMFANL: Notebook for my new solver book](https://github.com/ctkelley/NotebookSIAMFANL)**
>
> Notebook for my new solver book. Contribute to ctkelley/NotebookSIAMFANL development by creating an account on GitHub.
---
### Author:  [@Maria95](https://discourse.julialang.org/u/Maria95)
#### Post date: [December 1, 2020, 5:16pm UTC](https://discourse.julialang.org/t/nlsolve-false-convergence/50922/7 "2020-12-01T17:16:15Z")
> [@ctkelley](#):
>
> I’m not clear on what your code is doing. In any case, if you are solving a system of nonlinear equations
>
> F(x)=0
Yes, it is solving for F(x) = 0
The code is in the OP with the last two lines replace by the code below. This applies the convergence based on norm of the residuals
```julia
res = nlsolve(f!, j!, [0.01];method =:anderson,show_trace=false,beta=1.0,ftol=1E-10,xtol=1E-12)
convergence_criteria(res) = res.residual_norm <= 1.0e-10
x _res = Float64
if convergence_criteria(res) == true
x_res = res.zero[1]
else x_res = "Error"
end
```
Thanks for providing links to your notebooks. Looks really good