Add limited memory broyden implementation

[avik-pal]

This is not too useful (and will be slower than Broyden) on small problems. But it scales quite well.

julia> using SimpleNonlinearSolve

julia> f = (u, p) -> u .* u .- 2.0;
julia> probN = NonlinearProblem(f, ones(1000));

julia> @benchmark sol = solve(probN, Broyden())
BenchmarkTools.Trial: 97 samples with 1 evaluation.
 Range (min … max):  45.189 ms … 72.033 ms  ┊ GC (min … max): 6.37% … 8.07%
 Time  (median):     51.164 ms              ┊ GC (median):    8.35%
 Time  (mean ± σ):   51.708 ms ±  4.675 ms  ┊ GC (mean ± σ):  8.29% ± 1.78%

    █ ▁▆▁ ▁▃▁▁ ▃ ▃█▆  ▁    █▁                                  
  ▇▄█▇███▁████▄█▁███▇▇█▄▄▇▇██▇▇▄▇▁▇▄▁▄▁▄▄▁▄▇▁▄▁▄▁▁▁▁▁▁▁▁▁▁▁▁▄ ▁
  45.2 ms         Histogram: frequency by time          66 ms <

 Memory estimate: 130.39 MiB, allocs estimate: 126.

julia> @benchmark sol = solve(probN, LBroyden())
BenchmarkTools.Trial: 4978 samples with 1 evaluation.
 Range (min … max):  692.494 μs …   3.050 ms  ┊ GC (min … max):  0.00% … 58.68%
 Time  (median):     855.718 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   987.179 μs ± 388.915 μs  ┊ GC (mean ± σ):  11.79% ± 16.94%

   ▁▃▅██▇▆▆▅▄▃▃▂▁                                     ▁▂▂▂▁▁▁▁  ▂
  ▆███████████████▇▆▅▃▄▁▁▁▃▁▃▃▄▁▁▃▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▆███████████ █
  692 μs        Histogram: log(frequency) by time       2.34 ms <

 Memory estimate: 3.85 MiB, allocs estimate: 415.

[codecov]

Codecov Report

Merging #41 (c00b3b3) into main (a748c90) will increase coverage by 0.11%.
The diff coverage is 94.00%.

@@            Coverage Diff             @@
##             main      #41      +/-   ##
==========================================
+ Coverage   92.70%   92.81%   +0.11%     
==========================================
  Files          12       13       +1     
  Lines         507      557      +50     
==========================================
+ Hits          470      517      +47     
- Misses         37       40       +3     

Impacted Files	Coverage Δ
src/SimpleNonlinearSolve.jl	0.00% <ø> (ø)
src/lbroyden.jl	94.00% <94.00%> (ø)

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[ChrisRackauckas]

If it's main use is for bigger equations, maybe setup the loop to use cached arrays.

[avik-pal]

The tests probably need to be fixed. They will fail if the solver finds the "other" solution.