What is the concept of numerical methods for solving linear algebra in Numerical Analysis?

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What is the concept of numerical methods for solving linear algebra in Numerical Analysis?

The concept of numerical methods for solving linear algebra in Numerical Analysis involves using mathematical algorithms and techniques to approximate solutions to systems of linear equations. These methods aim to find numerical solutions that are close to the exact solutions, which may not always be feasible to obtain analytically. Some commonly used numerical methods for solving linear algebra problems include Gaussian elimination, LU decomposition, and iterative methods such as Jacobi and Gauss-Seidel. These methods involve performing various operations on the given system of equations to reduce it to a simpler form or iteratively improving an initial guess until a desired level of accuracy is achieved.