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Numerical Analysis | 1. Introduction

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Slides based on "Inleiding tot de numerieke wiskunde" by Prof. Dr. Adhemar Bultheel and course notes by Prof. Dr. Marc Van Barel.

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Numerical Analysis | 1. Introduction

  1. 1. Numerical Analysis Introduction
  2. 2. Overview • • • • Definition Inaccuracy Example Numerical method to algorithm
  3. 3. Definition • The study of algorithms that use numerical approximation
  4. 4. Inaccuracy • Inaccurate data • Rounding errors • Infinite amount of operations
  5. 5. Example • x² - 742x + 2 = 0
  6. 6. Example Quadratic_equation < in: b, c out: x1 , x2 > D  [ (b/2)² – c ]1/2 x1  –b/2 + D x2  –b/2 – D
  7. 7. Example
  8. 8. Example • Alternative to finding x2 : x2 = c / x 1 = 2 / 741.997 = 0.26953 * 10–2
  9. 9. Numerical method to algorithm • Distinction between numerical methods: ▫ Accuracy (numerical stability) ▫ Efficiency  Design of an algorithm
  10. 10. Overview • • • • Definition Inaccuracy Example Numerical method to algorithm
  11. 11. Sources • “Inleiding tot de numerieke wiskunde”, A. Bultheel, 2007, Acco • http://en.wikipedia.org/wiki/Numerical_analysis By knowledgedriver, 2012.

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