The characteristics of numerical analysis include accuracy (the numerical value should be as accurate as possible), robustness (the algorithm should be able to solve many problems, and the user should be concerned when the result is inaccurate) and speed (the faster the calculation, the better the method). The calculation method itself introduces some numerical analysis methods suitable for computers. These methods are based on mathematical analysis, algebra, differential equations and other mathematical theories. According to the characteristics that students in our school pay more attention to basic theory, the numerical analysis method expounds the mathematical theoretical basis of the method as clearly as possible while introducing the method, and proves the related introduction of the method strictly and concisely. The methods in numerical analysis are relatively independent, but as a course, we try to compile it into a relatively coherent and complete teaching material.

Singular value of matrix is a mathematical concept, which is generally obtained by singular value decomposition (SVD decomposition for short). If we want to ask what singular value means, we must consider the corresponding meaning of singular value in different practical engineering applications. We try to avoid strict deduction of mathematical symbols and start intuitively from a picture. Let's see what singular value means.

Numerical analysis is a branch of mathematics, which studies and analyzes the numerical calculation methods and theories of solving mathematical problems with computers. It takes the theory and method of solving mathematical problems by digital computer as the research object and is the main part of computational mathematics. To calculate the orbit of spacecraft, numerical solutions of ordinary differential equations are required. Many advanced numerical analysis methods will be used for numerical weather forecast.