1. **'''Error Analysis**''': Understanding and minimizing the errors that arise in numerical calculations, such as round-off errors, truncation errors, and approximation errors.
2. **'''Convergence**''': Determining whether a numerical method will converge to the correct solution as more iterations or finer steps are taken.
3. **'''Stability**''': Ensuring that small changes in the input or intermediate steps do not cause large changes in the output, which could lead to incorrect results.
4. **'''Efficiency**''': Developing algorithms that solve problems in a reasonable amount of time and with manageable computational resources.
5. **'''Conditioning**''': Analyzing how the solution to a problem is affected by small changes in the input data, which helps in assessing the reliability of the numerical solution.
Numerical analysis plays a crucial role in scientific computing, engineering simulations, financial modeling, and many other fields where mathematical modeling is essential.
