In previous work we introduced a construction to produce multiresolutions from given subdivisions. A portion of that construction required solving bilinear equations using a symbolic algebra system. Here we replace the bilinear equations with a pair of linear equation systems, resulting in a completely numerical construction. Diagrammatic tools provide assistance in carrying this out. The const...

We develop an intersection theory for a singular hermitian line bundle with positive curvature current on a smooth projective variety and irreducible curves on the variety. And we prove the existence of a natural rational fibration structure associated with the singular hermitian line bundle. Also for any pseudoeffective line bundle on a smooth projective variety, we prove the existence of a na...

Cointegration analysis involves the solution of a generalized eigenproblem involving moment matrices and inverted moment matrices. These formulae are unsuitable for actual computations because the condition numbers of the resulting matrices are unnecessarily increased. Our note discusses how to use the structure of the problem to achieve numerically stable computations, based on QR and singular...

where / is a smooth function. The basic theory of numerical methods for (1) has been known for more than thirty years, see e.g. [8]. This theory, in tandem with practical experimentation, has led to the development of general software packages for the efficient solution of (1). It is perhaps remarkable that both the theory and the packages do not take into account any structure the problem may ...

We study the numerical stability of polynomial based encoding methods, which has emerged to be a powerful class techniques for providing straggler and fault tolerance in area coded computing. Our contributions are as follows: 1)We construct new codes matrix multiplication that achieve same fault/straggler previously constructed MatDot Codes Polynomial Codes.2)We show condition number every m ×m...