What are the main objectives of Numerical Analysis?

The main objectives of Numerical Analysis are as follows:

1. Approximation: Numerical Analysis aims to develop methods and algorithms to approximate the solutions of mathematical problems that cannot be solved exactly. It focuses on finding numerical approximations that are accurate and efficient.

2. Error Analysis: Another objective of Numerical Analysis is to analyze and quantify the errors that arise during the process of numerical computation. It involves studying the sources of errors, understanding their behavior, and devising techniques to minimize or control them.

3. Stability and Convergence: Numerical Analysis investigates the stability and convergence properties of numerical methods. Stability refers to the ability of a method to produce reliable results in the presence of small perturbations or errors. Convergence refers to the behavior of a method as the number of iterations or steps increases, aiming to ensure that the approximations converge to the true solution.

4. Efficiency: Numerical Analysis aims to develop efficient algorithms and techniques that can solve mathematical problems in a computationally efficient manner. It involves optimizing the use of computational resources, such as time and memory, to obtain accurate results within reasonable timeframes.

5. Implementation and Software Development: Numerical Analysis involves the implementation of numerical methods and algorithms in computer programs. It focuses on developing robust and user-friendly software tools that can be used to solve a wide range of mathematical problems.

6. Application to Real-World Problems: Numerical Analysis aims to apply its methods and techniques to solve real-world problems from various fields, such as physics, engineering, finance, and computer science. It involves adapting and customizing numerical methods to specific problem domains, ensuring their applicability and effectiveness in practical scenarios.

Overall, the main objectives of Numerical Analysis revolve around developing accurate, efficient, and reliable numerical methods to solve mathematical problems, analyzing and controlling errors, ensuring stability and convergence, and applying these methods to real-world problems.