拟插值是数学和应用中函数和数据逼近的最有用和最常用的方法之一。它的优点是多方面的：准插值可以在任意维上进行近似，对于分散的、网格化的节点以及任意数量的数据，它们是有效的，并且相对容易制定。这本书为研究生和研究人员提供了该领域的介绍，概述了所有的数学背景和实现方法。拟插值的数学分析从三个方向给出，即基于进行近似的基（样条空间、径向基函数）、拟插值的形式和计算（点求值、平均值、最小二乘）以及数学性质（存在性、局部性、收敛性问题、精度）。了解在不同环境中使用哪种类型的准插值，以及如何优化其功能以适应物理和工程应用。
Quasi-Interpolation
Quasi-interpolation is one of the most useful and often applied methods for the approximation of functions and data in mathematics and applications. Its advantages are manifold: quasi-interpolants are able to approximate in any number of dimensions, they are efficient and relatively easy to formulate for scattered and meshed nodes and for any number of data. This book provides an introduction into the field for graduate students and researchers, outlining all the mathematical background and methods of implementation. The mathematical analysis of quasi-interpolation is given in three directions, namely on the basis (spline spaces, radial basis functions) from which the approximation is taken, on the form and computation of the quasi-interpolants (point evaluations, averages, least squares), and on the mathematical properties (existence, locality, convergence questions, precision). Learn which type of quasi-interpolation to use in different contexts and how to optimise its features to suit applications in physics and engineering.
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