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SciPy Recipes

You're reading from   SciPy Recipes A cookbook with over 110 proven recipes for performing mathematical and scientific computations

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Product type Paperback
Published in Dec 2017
Publisher Packt
ISBN-13 9781788291460
Length 386 pages
Edition 1st Edition
Languages
Tools
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Authors (3):
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V Kishore Ayyadevara V Kishore Ayyadevara
Author Profile Icon V Kishore Ayyadevara
V Kishore Ayyadevara
Ruben Oliva Ramos Ruben Oliva Ramos
Author Profile Icon Ruben Oliva Ramos
Ruben Oliva Ramos
Luiz Felipe Martins Luiz Felipe Martins
Author Profile Icon Luiz Felipe Martins
Luiz Felipe Martins
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Table of Contents (11) Chapters Close

Preface 1. Getting to Know the Tools FREE CHAPTER 2. Getting Started with NumPy 3. Using Matplotlib to Create Graphs 4. Data Wrangling with pandas 5. Matrices and Linear Algebra 6. Solving Equations and Optimization 7. Constants and Special Functions 8. Calculus, Interpolation, and Differential Equations 9. Statistics and Probability 10. Advanced Computations with SciPy

Non-linear equations and systems

In the solution of linear equations and systems, f(x) = 0, we had the choice of using either direct methods or iterative processes. A direct method in that setting was simply the application of an exact formula involving only the four basic operations: addition, subtraction, multiplication, and division. The issues with this method arise when cancellation occurs, mainly whenever sums and subtractions are present. Iterative methods, rather than computing a solution in a finite number of operations, calculate closer and closer approximations to the said solution, improving the accuracy with each step.

In the case of non-linear equations, direct methods are seldom a good idea. Even when a formula is available, the presence of non-basic operations leads to uncomfortable rounding errors. Let's see this using a very basic example.

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