Short proofs of some theorems in approximation theory
نویسندگان
چکیده
منابع مشابه
Algebraic proofs of some fundamental theorems in algebraic K - theory
We present new proofs of the additivity, resolution and cofinality theorems for the algebraic K-theory of exact categories. These proofs are entirely algebraic, based on Grayson’s presentation of higher algebraic K-groups via binary complexes. 2000 Mathematics Subject Classification: 19D99
متن کاملShort proofs of classical theorems
We give proofs of Ore’s theorem on Hamilton circuits, Brooks’ theorem on vertex coloring, and Vizing’s theorem on edge coloring, as well as the Chvátal-Lovász theorem on semi-kernels, a theorem of Lu on spanning arborescences of tournaments, and a theorem of Gutin on diameters of orientations of graphs. These proofs, while not radically different from existing ones, are perhaps simpler and more...
متن کاملStatistical Proofs of Some Matrix Theorems
Books on linear models and multivariate analysis generally include a chapter on matrix algebra, quite rightly so, as matrix results are used in the discussion of statistical methods in these areas. During recent years a number of papers have appeared where statistical results derived without the use of matrix theorems have been used to prove some matrix results which are used to generate other ...
متن کاملNegative Theorems in Approximation Theory
1. INTRODUCTION. Negative theorems have a rich tradition in mathematics. In fact mathematics seems to be unique among the sciences in that negative results are very much a part of the mathematical edifice. Most mathematical theories try to explain what is possible and also what is not. To understand the structure of a mathematical theory is also to understand its limitations. There are many dif...
متن کاملComplexity theory, proofs and approximation
We give a short introduction to some questions in complexity theory and proceed to give some recent developments. In particular, we discuss probabilistically checkable proofs and their applications in establishing inapproximability results. In a traditional proof the proofchecker reads the entire proof and decides deterministically whether the proof is correct. In a probabilistically checkable ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2004
ISSN: 0021-9045
DOI: 10.1016/j.jat.2003.11.008