This paper introduces the paradigm of optimization under uncertainty for modelling and solving matrix nearness problems. In particular, it considers the concrete problem of recovering correlation matrices from uncertain observations by introducing two different approaches to tackling uncertainty. The first approach invokes the framework of robust optimization to construct low error solutions th...

concept of nearness (contiguity, proximity) between families of sets (finite families, pairs). Again F. Riesz in 1908 was the first to explore this path by defining a "Verkettung" between pairs of sets. He did not require A n B ~ ¢ ~ A is "near" B. Today one generally makes this assumption and thus obtains c (A) = [x: [x] is "near" A]. The assumptions CI , C2 , C3 follow from requirements usual...

thought allows us to transcend the particularities of our specific place. This ability allows us to look past our own species and enter into relationships with other animals that amount to more than simply seeing them as objects for our consumption. On the other hand, our closest biological relatives, the Neanderthals, failed to form relationships with other animals that approach anywhere near ...

We discuss three types of sparse matrix nearness problems: given a sparse symmetric matrix, find the matrix with the same sparsity pattern that is closest to it in Frobenius norm and (1) is positive semidefinite, (2) has a positive semidefinite completion, or (3) has a Euclidean distance matrix completion. Several proximal splitting and decomposition algorithms for these problems are presented ...

Matrix trace inequalities are finding increased use in many areas such as analysis, where they can be used to generalise several well known classical inequalities, and computational statistics, where they can be applied, for example, to data fitting problems. In this paper we give simple proofs of two useful matrix trace inequalities and provide applications to orthogonal regression and matrix ...

Many scientific computing algorithms (in various domains, such as weather prediction, structural analysis, or electrical network analysis) strongly rely on solving fundamental matrix computation problems (such as linear system solving, eigenvalue decomposition, singular value decomposition, matrix nearness problems, joint diagonalization of matrices...). These problems are often solved using it...

There is growing evidence that exposure to nature increases human well-being, including in urban areas. However, relatively few studies have linked subjective satisfaction objective features of the environment. In this study we explore links among environmental (tree cover, water, and bird diversity) judgements satisfaction. We surveyed residents Ottawa, Canada (n = 1035) about their with local...