On a progressive and iterative approximation method with memory for least square fitting

An Analysis of Students’ failing in University Based on Least Square Method and a New arctan − exp Logistic Regression Function

“…It is not easy to realize multivariate nonlinear fitting directly using partial least squares method, and it may cause large errors. erefore, with the help of existing research results [31,32], the multilevel least square method is used to fit the curve, and use the N + 1 term to predict the difference between the real value of the N term and the predicted value, so as to achieve the approximate effect.…”

Generalized and optimal sequence of weights on a progressive‐iterative approximation method with memory for least square fitting

“…With a point set $$$ {\left\{{Q}_j\right\}}_{j=1}^m $$$ and starting control point set $$$ {\left\{{P}_i^0\right\}}_{i=1}^n $$$, the PIA method assigned in Lin et al, 16 the LSPIA method in Deng and Lin, 7 and the MLSPIA method in Huang and Wang 17 approximate the curves or surfaces repetitively with the NTP basis as follows: $$$$ {C}^{k+1}(t)=\sum \limits_{i=1}^n{B}_i(t){P}_i^{k+1},\kern2em t\in \left[0,1\right],\kern2em k\ge 0, $$$$ the control points are updated $$$$ {P}_i^{k+1}={P}_i^k+{\Delta}_i^k,\kern2em i\in \left\{1,2,3,\dots, n\right\},\kern2em k\ge 0, $$$$ with adjusting the vector …”

“…The memory for least square fitting PIA method (MLSPIA) is a least square form of the PIA method 16 and the LSPIA method 7 created directly in Huang and Wang 17 to enhance convergence rate. It repeatedly estimates control points and creates a sequence of converging curves to arrive at a least square fitting solution.…”

“…• The GOLSPIA method includes the GLSPIA method using the sequences of weights, which is generalized to the multidimensional of the MLSPIA method. 17 • The GOLSPIA method can converge faster than the MLSPIA method 17 from the viewpoint of the iterative steps and the error in each iterative step. • Whether or not the collocation matrix has a deficient column rank, the GOLSPIA method is feasible.…”

“…The MLSPIA method, which is a least square form of the PIA method 16 and the LSPIA method 7 produced directly, 17 is one of the LSF methods. By repeatedly approximating control points and generating a series of converging curves or surfaces, it arrives to a LSF solution.…”