Solving Overdetermined Matrices Without SVD

[Youvan]

Attached, you will find a formula-based solution for an overdetermined logical matrix pseudoinverse. This simple formula gives the same result as the Moore-Penrose method. Does anyone know of any other overdetermined matrices that can be solved without using SVD methods?

 

[jvicens]

Thank you for sharing this formula-based solution for an overdetermined logical matrix pseudoinverse. It is interesting to see that it yields the same result as the more commonly used Moore-Penrose method.

To answer your question, there are indeed other methods for solving overdetermined matrices without using SVD. One such method is the least squares method, which involves finding the minimum sum of squared errors between the actual data and the predicted values. This method is commonly used in regression analysis and can also be applied to overdetermined matrices.

Another approach is the QR decomposition method, which decomposes the matrix into an upper triangular matrix and an orthogonal matrix. This method can be used to solve overdetermined matrices by finding the least squares solution using the triangular matrix.

There are also iterative methods such as the Gauss-Seidel method and the Jacobi method, which can be used to solve overdetermined matrices by iteratively updating the solution until convergence is achieved.

Overall, there are multiple methods available for solving overdetermined matrices without using SVD. Each method may have its own advantages and limitations, so it is important to carefully consider the specific problem at hand when choosing a method.