| F04MEF | Update solution of the Yule–Walker equations for real symmetric positive-definite Toeplitz matrix |
| F04MFF | Update solution of real symmetric positive-definite Toeplitz system |
| F06FJF | Update Euclidean norm of real vector in scaled form |
| F06KJF | Update Euclidean norm of complex vector in scaled form |
| F06PMF | Rank-1 update, real rectangular matrix |
| F06PPF | Rank-1 update, real symmetric matrix |
| F06PQF | Rank-1 update, real symmetric packed matrix |
| F06PRF | Rank-2 update, real symmetric matrix |
| F06PSF | Rank-2 update, real symmetric packed matrix |
| F06QPF | QR factorization by sequence of plane rotations, rank-1 update of real upper triangular matrix |
| F06SMF | Rank-1 update, complex rectangular matrix, unconjugated vector |
| F06SNF | Rank-1 update, complex rectangular matrix, conjugated vector |
| F06SPF | Rank-1 update, complex Hermitian matrix |
| F06SQF | Rank-1 update, complex Hermitian packed matrix |
| F06SRF | Rank-2 update, complex Hermitian matrix |
| F06SSF | Rank-2 update, complex Hermitian packed matrix |
| F06TBF | Rank-1 update, complex symetric matrix |
| F06TDF | Rank-1 update, complex symetric packed matrix |
| F06TPF | QR factorization by sequence of plane rotations, rank-1 update of complex upper triangular matrix |
| F06YPF | Rank-k update of a real symmetric matrix |
| F06YRF | Rank-2k update of a real symmetric matrix |
| F06ZPF | Rank-k update of a complex Hermitian matrix |
| F06ZRF | Rank-2k update of a complex Hermitian matrix |
| F06ZUF | Rank-k update of a complex symmetric matrix |
| F06ZWF | Rank-2k update of a complex symmetric matrix |
| G02BTF | Update a weighted sum of squares matrix with a new observation |
| G13AGF | Univariate time series, update state set for forecasting |
| G13BGF | Multivariate time series, update state set for forecasting from multi-input model |
| G13EAF | Combined measurement and time update, one iteration of Kalman filter, time-varying, square root covariance filter |
| G13EBF | Combined measurement and time update, one iteration of Kalman filter, time-invariant, square root covariance filter |