Improvements for Broyden and Klement

[avik-pal]

See JuliaNLSolvers/NLsolve.jl#287

Needs #297 to go in first

Fixes #260

Summary

1. Broyden and Klement can (re-)start with the true (inv-)jacobian if asked for
2. For Broyden, it improves robustness but makes Klement even more unstable for ill-conditioned problems
3. Klement with identity initialization makes the Jacobian always diagonal; the updated solver exploits this and is significantly faster
4. Klement for non-diagonal jacobians resets the jacobian if the jacobian is "too" ill-conditioned; this improves the stability somewhat
5. Bad Broyden Update Rule
6. Klement with true jacobian diagonal initialization
7. Initial Scaling factor to improve stability

TODOs

• Diagonal Update Rule for Broyden
• Exciting Mixing Update Rule for Broyden
• Testing

[codecov]

Codecov Report

Attention: 44 lines in your changes are missing coverage. Please review.

Comparison is base (021901e) 88.01% compared to head (c4bde4d) 86.08%.
Report is 2 commits behind head on master.

Files	Patch %	Lines
src/utils.jl	69.87%	25 Missing ⚠️
src/broyden.jl	90.27%	7 Missing ⚠️
src/klement.jl	91.25%	7 Missing ⚠️
src/trace.jl	25.00%	3 Missing ⚠️
src/NonlinearSolve.jl	33.33%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #303      +/-   ##
==========================================
- Coverage   88.01%   86.08%   -1.94%     
==========================================
  Files          21       21              
  Lines        1669     1825     +156     
==========================================
+ Hits         1469     1571     +102     
- Misses        200      254      +54     

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[avik-pal]

This should be good as well!