A new algorithm to approximate Hermitian matrices by positive semidefinite matrices based on modified Cholesky decompositions is presented. The approximation error and the condition number of the approximation can be controlled by parameters of the algorithm. The algorithm tries to minimize the approximation error in the Frobenius norm. It has no significant runtime and memory overhead compared to the computation of an unmodified Cholesky decomposition. Sparsity and positive diagonal entries can be preserved. Numerical optimization and statistics are two fields of application in which the algorithm can be a great improvement.
Bundle-based similarity measurement for positive semidefinite matrices
Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices
The Estimation of Approximation Error using the Inverse Problem and the Set of Numerical Solutions
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