Multivariate approximation

多元近似

• 批准号: 372001-2010
• 负责人: Prymak, Andriy
• 金额: $ 1.24万
• 依托单位: University of Manitoba
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508658
• 关键词: Multivariate; approximation

Approximation theory studies the ability to approximate general, possibly complicated, functions by simpler and more easily calculated functions. Many problems in approximation theory of functions of one variable have been solved. However, the methods do not always easily generalize to the approximation of functions of several variables. The main goal of my proposed research is to develop existing and create new methods for the approximation of functions of several variables. I will focus on questions related to measures of smoothness (how can we easily measure or "predict" the accuracy of approximation) and shape preserving approximation (if the target function has a certain shape, how to construct an approximation which also possesses such a shape).

近似理论研究用更简单和更容易计算的函数来近似一般的，可能复杂的函数的能力。一元函数逼近论中的许多问题已得到解决。然而，这些方法并不总是容易推广到多元函数的逼近。我所提出的研究的主要目标是发展现有的和创建新的方法，用于逼近多个变量的函数。我将专注于与光滑度（我们如何能够轻松地测量或“预测”近似的准确性）和保形近似（如果目标函数具有某种形状，如何构造一个也具有这种形状的近似）相关的问题。