Block Lanczos tridiagonalization of complex symmetric matrices
Sanzheng Qiao, Guohong Liu, W. L. Xu · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
The classic Lanczos method is an effective method for tridiagonalizing real symmetric matrices. Its block algorithm can significantly improve performance by exploiting memory hierarchies. In this paper, we present a block Lanczos method for tridiagonalizing complex symmetric matrices. Also, we propose a novel componentwise technique for detecting the loss of orthogonality to stablize the block Lanczos algorithm. Our experiments have shown our componentwise technique can reduce the number of orthogonalizations.