Prospectus for the next LAPACK and ScaLAPACK libraries
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
A scalable, numerically stable, high-performance tridiagonal solver using GPUs
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
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We present one more algorithm to compute the condition number (for inversion) of an n X n tridiagonal matrix J in O(n) time. Previous O(n) algorithms for this task given by Higham [SIAM J. Sci. Statist. Comput., 7 (1986), pp. 150--165] are based on the tempting compact representation of the upper (lower) triangle of J-1 as the upper (lower) triangle of a rank-one matrix. However they suffer from severe overflow and underflow problems, especially on diagonally dominant matrices. Our new algorithm avoids these problems and is as efficient as the earlier algorithms.