Computing P–summing Norms with Few Vectors
نویسندگان
چکیده
It is shown that the p-summing norm of any operator with n-dimensional domain can be well-aproximated using only " few " vectors in the definition of the p-summing norm. Except for constants independent of n and log n factors, " few " means n if 1 < p < 2 and n p/2 if 2 < p < ∞.
منابع مشابه
A remark on p-summing norms of operators
In this paper we improve a result of W. B. Johnson and G. Schechtman by proving that the p-summing norm of any operator with n-dimensional domain can be well-approximated using C(p)n logn(log logn)2 vectors if 1 < p < 2, and using C(p)np/2 logn if 2 < p <∞. 1. p-summing norms Throughout this paper we will follow notations of N. Tomczak-Jaegermann [To]. Definition 1.1. Let X and Y be Banach spac...
متن کاملUse of Structure Codes (Counts) for Computing Topological Indices of Carbon Nanotubes: Sadhana (Sd) Index of Phenylenes and its Hexagonal Squeezes
Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sa...
متن کاملFirst-order System Least-squares Methods for Partial Differential Equations
In recent years there has been lots of interest in the use of first-order system leastsquares method (FOSLS) for numerical approximations of elliptic partial differential equations, Stokes equations, elasticity and Navier-Stokes equations. In this paper we will provide a brief review of FOSLS around elliptic problems and Stokes equations. FOSLS is to find a minimization solution which minimizes...
متن کاملVoronoi Cells of Lattices with Respect to Arbitrary Norms
Motivated by the deterministic single exponential time algorithm of Micciancio and Voulgaris for solving the shortest and closest vector problem for the Euclidean norm, we study the geometry and complexity of Voronoi cells of lattices with respect to arbitrary norms. On the positive side, we show that for strictly convex and smooth norms the geometry of Voronoi cells of lattices in any dimensio...
متن کاملNonlinear Approximation and Image Representation using Wavelets
We address the problem of finding sparse wavelet representations of high-dimensional vectors. We present a lower-bounding technique and use it to develop an algorithm for computing provably-approximate instance-specific representations minimizing general `p distances under a wide variety of compactly-supported wavelet bases. More specifically, given a vector f ∈ R, a compactly-supported wavelet...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1994