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A preconditioned Newton algorithm for the nearest correlation matrix. (English) Zbl 1188.65055

The authors present several improvements made on a Newton algorithm for computing the correlation matrix nearest in the Frobenius norm to a given matrix. The usage of MINRES solver instead of the conjugate gradient method and a Jacobi type preconditioner for the Newton equations lead to a significant speed-up over the original algorithm and allow the solution of problems of dimension a few thousand in a few tens of minutes.

MSC:

65F30 Other matrix algorithms (MSC2010)

Software:

QSDP; mctoolbox
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