# Updating the singular value decomposition

With this observation, in this paper, we present an efficient method for updating Singular Value Decomposition of rank-1 perturbed matrix in $O(n^2 \ \text(\frac))$ time.The method uses Fast Multipole Method (FMM) for updating singular vectors in $O(n \ \text (\frac))$ time, where $\epsilon$ is the precision of computation.There are two versions of the known issues list available: Known Issues by Category Known Issues by Date Please refer to White Paper "Lab VIEW Known Issues Categories Defined" for an explanation of the categories. This will load the new version into memory prior to you requesting the older version.

However, maintaining the covariance matrix is not feasible computationally for high-dimensional systems. En KFs represent the distribution of the system state using a collection of state vectors, called an ensemble, and replace the covariance matrix by the sample covariance computed from the ensemble.

The ensemble is operated with as if it were a random sample, but the ensemble members are really not independent – the En KF ties them together.

One advantage of En KFs is that advancing the pdf in time is achieved by simply advancing each member of the ensemble.

The ensemble Kalman filter (En KF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models.

The En KF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting.

However, maintaining the covariance matrix is not feasible computationally for high-dimensional systems. En KFs represent the distribution of the system state using a collection of state vectors, called an ensemble, and replace the covariance matrix by the sample covariance computed from the ensemble.The ensemble is operated with as if it were a random sample, but the ensemble members are really not independent – the En KF ties them together.One advantage of En KFs is that advancing the pdf in time is achieved by simply advancing each member of the ensemble.The ensemble Kalman filter (En KF) is a recursive filter suitable for problems with a large number of variables, such as discretizations of partial differential equations in geophysical models.The En KF originated as a version of the Kalman filter for large problems (essentially, the covariance matrix is replaced by the sample covariance), and it is now an important data assimilation component of ensemble forecasting.En KF is related to the particle filter (in this context, a particle is the same thing as ensemble member) but the En KF makes the assumption that all probability distributions involved are Gaussian; when it is applicable, it is much more efficient than the particle filter.