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Old Question Let suppose to have a covariance matrix $\boldsymbol$.The spectral decomposition of a positive definite matrix tells us that we can write $$ \boldsymbol = \boldsymbol\boldsymbol\boldsymbol\boldsymbol' $$ where the column vectors of $\boldsymbol$ are the normalized eigenvectors and $\boldsymbol$ is a diagonal matrix where the $i^$ element is the square root of the eigenvalue associated to the $i^$ normalized eigenvector. I found an algorithm for updating inverse of a matrix after small norm update using regression interpretation of inverse of covariance matrix, so I assumed something similar should exist for eigenvectors. I have 8k features and millions of datapoints, so covariance is approximate. Gradient update depends on eigenvalues of certain covariance matrix, and this covariance matrix changes at each step A naive approach is to use the eigenvalue solution of your matrix $A(t)$ as the initial guess of an iterative eigensolver for matrix $A(t \delta t)$. New iterative methods for solutions of the eigenproblem. This site stores nothing other than an automatically generated session ID in the cookie; no other information is captured.

recursive updating the eigenvalue decomposition of a covariance matrix-84recursive updating the eigenvalue decomposition of a covariance matrix-28

There is of course a large body of literature on eigenvalue perturbation that you may want to look at (see the other answer).My design of Extended Kalman filter is for a Heavy vehicle dynamics wherein I need to estimate grade and mass using the filter and velocity sensor only with Torque as the control input.I have completed the coding but need to tune the covariance matrices P, Q & R for error,process and measurement covariance.Then the covariance between $\boldsymbol_$ and $\boldsymbol_$ is given by $$ \sum_^K \mathbf_k [\mathbf_k]_ $$ As you can see, the choice of $\mathbf$ influences the covariance structure of my problem, and different $\mathbf$'s give different models.For example we can define $\mathbf$ to be the Cholesky factorization, but then it is easy to see that we are saying that, marginally, the covariance matrix of $\boldsymbol_1$ depends only on $\mathbf_1$, the one of $\boldsymbol_2$ depends on $\mathbf_1$ and $\mathbf_2$ and so on.

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