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Computing Numerically with Functions Instead of Numbers

Computing Numerically with Functions Instead of Numbers, illustration


Science and engineering depend upon computation of functions such as flow fields, charge distributions, and quantum states. Ultimately, such computations require some kind of discretization, but in recent years, it has become possible in many cases to hide the discretizations from the user. We present the Chebfun system for numerical computation with functions, which is based on a key idea: an analogy of floating-point arithmetic for functions rather than numbers.

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1. Introduction

The oldest problem of computing is, how can we calculate mathematical quantities? As other aspects of computing have entered into every corner of our lives, mathematical computation has become a less conspicuous part of computer science, but it has not gone away. On the contrary, it is bigger than ever, the basis of much of science and engineering.


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