Yuri Morozov

Chase and Trim: Earlier Deflation in Bidiagonal QR for the SVD

Chase and Trim (CAT) extends the bidiagonal QR algorithm for computing singular values and singular vectors by introducing additional deflation opportunities between QR sweeps. For selected interior superdiagonal couplings, CAT applies a local 2×2 singular value decomposition usi...

Chase And Trim (CAT): Active One-Rotation Deflation for the Symmetric QR Eigenvalue Algorithm

Chase And Trim (CAT) extends symmetric tridiagonal QR by creating additional deflation opportunities between QR sweeps. When a selected first-band coupling has not yet passed conventional deflation, CAT tests whether one local Jacobi rotation can annihilate it while creating only...

Householder Tridiagonalization as Preprocessing for the Jacobi Eigenvalue Algorithm

Householder tridiagonalization is not normally used before a Jacobi eigensolver because the reduction costs O(n³), while subsequent Jacobi rotations do not preserve the zeros it creates. We show that this argument does not settle whether preprocessing can nevertheless reduce the...