Computing the Zeros of Analytic Functions

1. Front Matter

   Pages I-VII

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2. Zeros of analytic functions

   • Peter Kravanja, Marc Van Barel

   Pages 1-59

3. Clusters of zeros of analytic functions

   • Peter Kravanja, Marc Van Barel

   Pages 61-81

4. Zeros and poles of meromorphic functions

   • Peter Kravanja, Marc Van Barel

   Pages 83-89

5. Systems of analytic equations

   • Peter Kravanja, Marc Van Barel

   Pages 91-103

6. Back Matter

   Pages 105-112

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Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

• Complex analysis
• Meromorphic function
• analytic function
• computational complex analysis
• formal orthogonal polynomials
• numerical analysis
• rational interpolation
• zeros of analytic functions

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