# Solving Overdetermined Matrices Without SVD

• MHB
• Youvan
In summary, there are various alternatives to SVD for solving overdetermined matrices, such as the least squares method, QR decomposition, and iterative methods like Gauss-Seidel and Jacobi.
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?

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• YI = PI.png
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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.

## 1. How does solving overdetermined matrices without SVD work?

Solving overdetermined matrices without SVD involves using a variety of mathematical techniques, such as least squares regression, to find the best possible solution for a system of equations with more equations than unknowns.

## 2. Why would someone want to solve overdetermined matrices without SVD?

Solving overdetermined matrices without SVD can be useful in situations where SVD may not be applicable or efficient, such as when dealing with large datasets or when the matrix is not well-conditioned.

## 3. What are the limitations of solving overdetermined matrices without SVD?

One limitation is that the solution obtained may not be unique, meaning there could be multiple solutions that fit the given system of equations. Additionally, the solution may not be the most accurate or optimal compared to using SVD.

## 4. What are some common techniques used for solving overdetermined matrices without SVD?

Some common techniques include least squares regression, QR decomposition, and the pseudoinverse matrix method. Each of these methods has its own advantages and disadvantages, and the choice of technique may depend on the specific problem at hand.

## 5. Can solving overdetermined matrices without SVD be applied to real-world problems?

Yes, solving overdetermined matrices without SVD has many practical applications in fields such as statistics, engineering, and data analysis. It can be used to solve problems involving linear regression, data fitting, and signal processing, among others.

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