Second-Order Polynomial Estimation of Response Surfaces Using Least Squares Method
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This paper presents a second-order polynomial estimation for response surfaces using the least squares method. The algorithm demonstrates high precision through its implementation of matrix operations for solving normal equations (typically implemented as (X'X)^{-1}X'y in MATLAB/Python). The method's flexibility allows seamless substitution of our provided 3D dataset with any alternative three-dimensional data through simple input parameter modifications. Our experimental framework incorporates cross-validation techniques to ensure robustness across diverse datasets. The research establishes that least-squares-based polynomial estimation serves as a high-accuracy approach for response surface modeling, providing a foundational methodology for further investigations in computational mathematics and data fitting applications. Key implementation aspects include polynomial feature expansion and regularization parameter tuning for improved numerical stability.
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