[denizd1]

Correctness

• RK45: error estimate was normalized twice; step control now uses one
  scaled error norm with exponent 1/5, h_min checks the unclipped step and
  raises ConvergenceError
• ODESolver.solve no longer shrinks h; time grid t0 + k*h, exact t_end,
  backward integration, systems of ODEs (vector states)
• Multistep methods: bootstrap stays inside [t0, t_end], cached f values,
  variable-step weights for a shortened last step; AdamsMoulton is now a
  real 2-step method (steps=1 gives the trapezoidal rule)
• Implicit methods raise ConvergenceError when Newton fails
• Bisection handles roots at the end points, relative tolerance, sign tests
• PowerIteration uses a fixed pseudo-random start vector; norm2 and
  condition_number("2") use singular values
• RQI and inverse iteration handle exactly singular shifts
• QREigenvalues: Hessenberg + Francis double-shift QR (complex pairs);
  shifted=False keeps the basic iteration
• SVD: one-sided Jacobi thin SVD, orthonormal U for rank-deficient A
• NonlinearFit: L2 objective, only improving steps accepted, augmented QR
  step, input validation, converged flag, verbose implemented
• Scale-aware pivot/rank/symmetry tests; QRSolver for tall matrices;
  LeastSquaresSolver/PolyFit reject m < n; classical Gram-Schmidt now
  projects the original columns
• Matrix/Vector: ==, unary -, scalar /, A[i], iteration, shape of empty
  matrices, ValueError on dimension mismatch

Performance

• Optional step recording (record_steps), permutation vector in LU,
  inverse iteration factorizes once, faster matmul/matvec, one matvec per
  power iteration, cached Cholesky L^T, barycentric Lagrange, PolyFit in a
  scaled variable with Horner evaluation

New features

• SOR, LU.det/inverse, Brent, RegulaFalsi (Illinois), CubicSpline,
  chebyshev_nodes, n-point and composite Gauss-Legendre, AdaptiveSimpson,
  Romberg, DormandPrince, auto step size for finite differences,
  plot helpers accept an axis

Project

• Test suite for every module (144 tests), demo smoke test, GitHub Actions
  workflow, version 0.2.0, optional extras, README update
• Tutorials updated for the new behaviour and re-executed

Co-Authored-By: Claude Opus 5.5 noreply@anthropic.com
Claude-Session: https://claude.ai/code/session_01AiW6XDeDLFt46PLZsaSF2h