Computing Positive Semidefinite Multigroup Nuclear Data Covariances

We propose a novel application of a method to compute the nearest positive semidefinite matrix. When applied to covariance matrices of multigroup nuclear data, the method removes unphysical components of the covariances while preserving the physical components of the original covariance matrix. The result is a mathematically proper covariance matrix.

We show that the method preserves the so-called zero sum rule of covariances of distributions in exact arithmetic. The results also hold for typical cases of finite precision arithmetic. We identify conditions that might damage the zero sum rule.

Rounding can distort the eigenvalues of a symmetric matrix. We give a known bound on how large distortions can occur due to round-off. Consequently, there is a known upper bound on how large negative eigenvalues can be attributed to round-off error. Current evaluations and processing codes do produce larger negative eigenvalues.

Three practical examples are processed and analyzed. We demonstrate that satisfactory results can be achieved.

We discuss briefly the relevance of the method, its properties, and alternative approaches. The method can be used as a part of a quality assurance program and would be a valuable addition to nuclear data processing codes.