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Enhanced Levenberg-Marquardt Algorithm with Residual Function Support #1116

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This PR implements:

  • Support for direct residual functions in Levenberg-Marquardt algorithm
  • Improved MINPACK-style control flow for damping parameter updates
  • Comprehensive statistical metrics in NonlinearMinimizationResult
  • Numerical differentiation through dedicated NumericalJacobian class

Closes #1114

…r reflect its purpose in modeling optimization problems
- Add configurable accuracy with orders 1-6 for both model and residual functions
- Use NumericalJacobian class for more reliable derivative approximation
- TStatistics and PValues for parameter significance testing
- ConfidenceIntervalHalfWidths for parameter precision
- Dependencies to measure parameter correlations
- Goodness-of-fit statistics
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diluculo commented Mar 22, 2025

Lastly, I've added a new ParameterStatistics class that computes all the key statistical measures for regression parameters, including standard errors, t-statistics, p-values, confidence intervals, and dependency analysis.

Ready for review and merge.

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Extend Levenberg-Marquardt Algorithm to Support Direct Function Minimization
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