Orthogonalization and Rayleigh-Ritz

virtual void chase::ChaseBase::QR(std::size_t fixednev, Base<T> cond) = 0

Performs QR factorization with optional Householder transformation.

This method performs a QR factorization on the matrix, optionally using Householder transformations for the computation.

Parameters:

  • fixednev – Total number of converged eigenpairs before the QR factorization.

  • cond – Condition number for controlling the factorization process.

virtual void chase::ChaseBase::RR(Base<T> *ritzv, std::size_t block) = 0

Performs Rayleigh-Ritz projection for eigenproblem reduction.

This method projects the eigenproblem into a smaller subspace, solves the smaller problem, and reconstructs the eigenvectors.

Parameters:

  • ritzv – Array to store the computed eigenvalues.

  • block – The number of non-converged eigenpairs used for the small eigenproblem.