Backward error analysis of the Lanczos bidiagonalization with reorthogonalization

Haibo Li, Guangming Tan, Tong Zhao

The $k$-step Lanczos bidiagonalization reduces a matrix $A\in {\mathbb{R}}^{m\times n}$ into a bidiagonal form $B_k\in {\mathbb{R}}^{(k+1)\times k}$ while generates two orthonormal matri…