Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles
Solving Transcendental Equations: The Chebyshev Polynomial Proxy and Other Numerical Rootfinders, Perturbation Series, and Oracles
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DOI：
10.1137/1.9781611973525
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发表时间：
2014-09
期刊：
影响因子：
--
通讯作者：
J. Boyd
中科院分区：
文献类型：
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作者：
J. Boyd
超越方程出现在科学和工程的每一个分支。虽然这些方程中的大多数都很容易求解，但有些却不容易，这就是本书作为跳伞运动员备用降落伞的数学等价物的地方-并不总是需要的，但当它是必不可少的。作者的目标是教艺术找到一个单一的代数方程或一对这样的方程的根。解决超越方程是独一无二的，因为它是第一本书来描述切比雪夫代理rootfinder，这是最可靠的方式来找到所有零的光滑函数的时间间隔，和非常可靠的频谱增强Weyl平分/行进三角形方法为二元rootfinding。它还包括三章分析方法-显式解，正则摄动展开，奇异摄动级数（包括超渐近）-不像其他书籍，只给出数值算法求解代数和超越方程。读者：这本书是为数值分析的专家而写的，也将吸引一般的数学家。它可以用于介绍和高级数值分析课程，并作为工程师和其他处理困难方程的参考。
Transcendental equations arise in every branch of science and engineering. While most of these equations are easy to solve, some are not, and that is where this book serves as the mathematical equivalent of a skydiver's reserve parachute - not always needed, but indispensible when it is. The author s goal is to teach the art of finding the root of a single algebraic equation or a pair of such equations. Solving Transcendental Equations is unique in that it is the first book to describe the Chebyshev-proxy rootfinder, which is the most reliable way to find all zeros of a smooth function on the interval, and the very reliable spectrally enhanced Weyl bisection/marching triangles method for bivariate rootfinding. It also includes three chapters on analytical methods - explicit solutions, regular pertubation expansions, and singular perturbation series (including hyperasymptotics) - unlike other books that give only numerical algorithms for solving algebraic and transcendental equations. Audience: This book is written for specialists in numerical analysis and will also appeal to mathematicians in general. It can be used for introductory and advanced numerical analysis classes, and as a reference for engineers and others working with difficult equations.