Davidson Algorithm¶

Overview¶

The Davidson algorithm is an iterative diagonalization method that is superior to Lanczos when you need multiple eigenvalues simultaneously. It builds a Krylov-like subspace but applies diagonal preconditioning to improve convergence.

API¶

import qkrylov as qk

result = qk.davidson_lowest(H, n_eig=3, max_subspace=20, tol=1e-8)
print(result.eigenvalues)   # first 3 eigenvalues
print(result.eigenvectors)  # corresponding eigenvectors

auto result = davidson_lowest(H, /*n_eig=*/3, /*max_subspace=*/20, /*tol=*/1e-8);
for (double e : result.eigenvalues) {
    std::cout << e << "\n";
}

Coming Soon¶

• Full parameter documentation
• Convergence analysis
• Comparison with Lanczos for multiple eigenvalues