Implement Conjugate Gradient (CG) for SPD systems

[tec-eli]

Description

Implement Conjugate Gradient (CG) to solve symmetric positive-definite (SPD)
linear systems A x = b without explicit factorization.

• Scope: src/krylov/conjugate_gradient.rs
• Signature: conjugate_gradient<T>(A: &SymmetricMatrix<T>, b: &Vector<T>, x0: &Vector<T>, max_iter: usize, tol: T) -> Result<Vector<T>, ConvergenceError>

Implementation notes

• Convergence rate depends on sqrt(κ(A)) — pair with high-condition-number matrices in
  tests to show graceful degradation.
• Only 4 fixed-size vectors (r, p, Ap, x), zero basis growth — stack-safe, no
  const-generic basis decision needed for this one.
• Don't try to prove SPD upfront (no cheap general test) — detect operationally (negative/
  ~zero p·Ap mid-iteration) and fail fast.
• max_iter is a mandatory hard cap, not optional.

Tasks

• Implement conjugate_gradient<T>(...)
• Monitor residual each iteration; early exit on convergence
• Detect non-SPD operationally and return Err, never panic
• Validate input dimensions (A.rows == A.cols == b.len() == x0.len())
• Add doc-comment with convergence guarantees and # Examples

Tests

• Unit tests: small SPD matrices with known solutions
• Property test: final residual ‖b - A x‖ is small
• Edge case: 1×1 system
• Edge case: ill-conditioned matrix (document degradation, not failure)
• Edge case: non-SPD input returns Err, not NaN/panic