Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied to fundamental frequency estimation. Such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid. In this paper, we therefore consider fast implementations of LCMV-based fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitz-like data covariance matrices, using as such either the classic time domain averaging covariance matrix estimator, or, if aiming for an increased spectral resolution, the covariance matrix resulting from the application of the recent iterative adaptive approach (IAA). The proposed exact implementations reduce the required computational complexity with several orders of magnitude, but, as we show, further computational savings can be obtained by the adoption of an approximative IAA-based data covariance matrix estimator, reminiscent of the recently proposed Quasi-Newton IAA technique. Furthermore, it is shown how the considered pitch estimators can be efficiently updated when new observations become available. The resulting time-recursive updating can reduce the computational complexity even further. The experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution. Finally, it is shown that the time-recursive implementations are able to track pitch fluctuations of synthetic as well as real-life signals. ; Recently, optimal linearly constrained minimum variance (LCMV) filtering methods have been applied to fundamental frequency estimation. Such estimators often yield preferable performance but suffer from being computationally cumbersome as the resulting cost functions are multimodal with narrow peaks and require matrix inversions for each point in the search grid. In this paper, we therefore consider fast implementations of LCMV-based fundamental frequency estimators, exploiting the estimators' inherently low displacement rank of the used Toeplitz-like data covariance matrices, using as such either the classic time domain averaging covariance matrix estimator, or, if aiming for an increased spectral resolution, the covariance matrix resulting from the application of the recent iterative adaptive approach (IAA). The proposed exact implementations reduce the required computational complexity with several orders of magnitude, but, as we show, further computational savings can be obtained by the adoption of an approximative IAA-based data covariance matrix estimator, reminiscent of the recently proposed Quasi-Newton IAA technique. Furthermore, it is shown how the considered pitch estimators can be efficiently updated when new observations become available. The resulting time-recursive updating can reduce the computational complexity even further. The experimental results show that the performances of the proposed methods are comparable or better than that of other competing methods in terms of spectral resolution. Finally, it is shown that the time-recursive implementations are able to track pitch fluctuations of synthetic as well as real-life signals.