Least Squares Method
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Resource Overview
The Least Squares Method is a mathematical optimization technique that finds the best functional match for data by minimizing the sum of squared errors. It provides a simple approach to estimate unknown parameters by ensuring the minimal squared difference between computed values and observed data. This method is widely used for curve fitting and can also express other optimization problems through energy minimization or entropy maximization. In implementation, it typically involves solving linear equations using matrix operations like numpy.linalg.lstsq() in Python or the backslash operator in MATLAB.
Detailed Documentation
The Least Squares Method is a mathematical optimization technique used to determine the optimal functional fit for data. Its core principle involves minimizing the sum of squared errors to achieve the best solution, thereby reducing discrepancies between calculated values and actual observations. This method not only simplifies the estimation of unknown parameters but also applies to optimization problems like curve fitting. Furthermore, it can express various other optimization challenges through energy minimization or entropy maximization, demonstrating broad practical applicability. In code implementation, the method often utilizes matrix algebra to solve normal equations, with key operations including covariance matrix calculation and gradient descent algorithms for nonlinear cases.
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