Updating the singular value decomposition

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For a survey of En KF and related data assimilation techniques, see G.

Evensen., called the prior, was evolved in time by running the model and now is to be updated to account for new data.

Let $A$ be a symmetric matrix with eigenvalue decomposition $UDU^T$. Has anything similar been done for the case where the update is of the form $A B$, where $B=uv^t vu^t$ is a rank-two symmetric matrix (note we can't just do two rank-one symmetric updates)?

have shown that given such an $A$, the eigenvalue decomposition of $A \rho xx^t$ may be computed efficiently.

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.

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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.

A manual relink of the properties/methods is required. NET assemblies in Lab VIEW, 1-dimension arrays of doubles or strings are represented as 2-dimension arrays of rank 1.

Workaround: N/A In recent versions of Lab VIEW, placing a constructor for a Folder Dialog Box object from Windows. Forms (4.0.0) will work successfully, but the containing VI will hang during execution. This can create an issue when the assembly is used in Visual Studio 2015 which will not accept 2-dimensional arrays of rank 1.

What if we relaxed the insistence that $B$ be symmetric and asked instead for an efficient computation of the SVD of the update $A B$?

References or thoughts would be greatly appreciated.

Not every issue known to NI will appear on this list; it is intended to only show the severe and common issues.

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