[deveshvaidyaofficial]

(ERROR) : PR Created once again,This PR is redundant [Check #3495 ]

Summary

Added implementation for the Interpolate-Truncate-Project (ITP) One Dimensional Solver algorithm for solving scalar nonlinear equations in Stan Math, addressing #3362

The solver will provide a safeguarded root-finding method that combines interpolation with truncation and projection while preserving a sign-changing bracket and the algorithm's convergence guarantees.

(Based on the Patch attached in the Issue description with the necessary changes made according to the requiremnts )

Tests

Targeted tests run locally on Windows:

• Primitive-mode solve_itp tests: 12 passed.
• Reverse-mode solve_itp tests: 4 passed.

Other Successful tests were:

• Bisection iteration count and the published cubic example.
• Lambert function example and variadic arguments.
• Endpoint roots and subnormal interval widths.
• Function evaluation bounds and final-width rounding behavior.
• Invalid brackets, invalid controls, insufficient iteration steps, and nonfinite function values.
• Reverse-mode implicit derivatives for scalar, variadic, and vector parameters.
• Rejection of singular implicit derivatives.

Side Effects

None

Release notes

Add an Interpolate-Truncate-Project (ITP) one dimensional root-finding solver to Stan Math for solving scalar nonlinear equations, with configurable convergence controls .

Checklist

• Copyright holder: Devesh Vaidya
  The copyright holder is typically you or your assignee, such as a university or company. By submitting this pull request, the copyright holder is agreeing to the license the submitted work under the following licenses:
  - Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
  - Documentation: CC-BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

• the basic tests are passing

  • unit tests pass (to run, use: ./runTests.py test/unit)
  • header checks pass, (make test-headers)
  • dependencies checks pass, (make test-math-dependencies)
  • docs build, (make doxygen)
  • code passes the built in C++ standards checks (make cpplint)

• the code is written in idiomatic C++ and changes are documented in the doxygen

• the new changes are tested