Computing the nearest correlation matrix to an indefinite estimate is a problem that comes from finance. Due to the computational expense of current software an alternative has recently been proposed called the Shrinking Method, developed by Higham et. al . This new method restores the definiteness of the approximate by elementwise perturbations. It proves to be extremely fast compared to computing the nearest, even for large matrices and a version of it has recently been included into the NAG Library. This has been the subject of my placement at NAG last summer and will be the topic of my dissertation.
 Nicholas J. Higham, Natasa Strabic, Vedran Sego. Restoring definiteness via shrinking, with an application to correlation matrices with a fixed block. MIMS EPrint 2014.54, Manchester Institute of Mathematical Sciences, The University of Manchester, UK, November 2014. 19 p.