Calculation of Schur complement returns matrix which is not positive semidefinite

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Evan 2017-5-25

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https://ww2.mathworks.cn/matlabcentral/answers/341920-calculation-of-schur-complement-returns-matrix-which-is-not-positive-semidefinite

编辑： Evan 2017-5-25

I'm trying to implement some basic Gaussian process regression. I know Matlab has functions that do this but I want to do a bit by hand so I feel more comfortable with the methods.

I'm using the following code to calculate the Schur complement to generate a covariance matrix for the data conditioned on the observations yObserv.

A = K(1:end-nObserv,1:end-nObserv);
B = K(1:end-nObserv,end-(nObserv-1):end);
C = K(end-(nObserv-1):end,end-(nObserv-1):end);
KSchur = A - B*(C\B');
mu = B*(C\(yObserv'));

Unfortunately, in some cases this expression returns a matrix which is not positive semidefinite, apparently due to numerical factors. The alternate strategy:

KSchur = A - B*inv(C)*B';

Has the same problem. I'm not experienced with such issues, so I'm hoping someone can suggest a way to formulate this operation to avoid the problem. Any suggestions?