Consider the following linear system of equations :

When solving this system using MATLAB, I found that the condition number of matrix is extremely large, indicating that the system is ill-conditioned. Some characteristics of the system are as follows:
Condition number of : 2.715e+06
Determinant of : 0.5196
I have attempted several methods, including least squares, normalization, and regularization, but none have produced satisfactory results in terms of accuracy. The matrix and is currently stored as double type, and I have also tried using ‘vpa’ to control the number of significant digits, but it was in vain. Are there any effective methods to solve this system, or is it possible to identify and eliminate highly correlated row vectors to ensure the accuracy of the remaining solutions?
Matlab data ‘.mat’:
https://1drv.ms/u/s!AlQCuPoSp7emgaNizYy43ea4fhgecg?e=vd3ubh
%% Load data
load("cal_linear_equations.mat");
%% Evaluate and calculate
DET_A=det(A_coeff);
Cond_A=cond(A_coeff);
Sol_real=A_coeffb_coeff;
Error=A_coeff*Sol_real-b_coeff;
max(abs(Error));Consider the following linear system of equations :

When solving this system using MATLAB, I found that the condition number of matrix is extremely large, indicating that the system is ill-conditioned. Some characteristics of the system are as follows:
Condition number of : 2.715e+06
Determinant of : 0.5196
I have attempted several methods, including least squares, normalization, and regularization, but none have produced satisfactory results in terms of accuracy. The matrix and is currently stored as double type, and I have also tried using ‘vpa’ to control the number of significant digits, but it was in vain. Are there any effective methods to solve this system, or is it possible to identify and eliminate highly correlated row vectors to ensure the accuracy of the remaining solutions?
Matlab data ‘.mat’:
https://1drv.ms/u/s!AlQCuPoSp7emgaNizYy43ea4fhgecg?e=vd3ubh
%% Load data
load("cal_linear_equations.mat");
%% Evaluate and calculate
DET_A=det(A_coeff);
Cond_A=cond(A_coeff);
Sol_real=A_coeffb_coeff;
Error=A_coeff*Sol_real-b_coeff;
max(abs(Error)); Consider the following linear system of equations :

When solving this system using MATLAB, I found that the condition number of matrix is extremely large, indicating that the system is ill-conditioned. Some characteristics of the system are as follows:
Condition number of : 2.715e+06
Determinant of : 0.5196
I have attempted several methods, including least squares, normalization, and regularization, but none have produced satisfactory results in terms of accuracy. The matrix and is currently stored as double type, and I have also tried using ‘vpa’ to control the number of significant digits, but it was in vain. Are there any effective methods to solve this system, or is it possible to identify and eliminate highly correlated row vectors to ensure the accuracy of the remaining solutions?
Matlab data ‘.mat’:
https://1drv.ms/u/s!AlQCuPoSp7emgaNizYy43ea4fhgecg?e=vd3ubh
%% Load data
load("cal_linear_equations.mat");
%% Evaluate and calculate
DET_A=det(A_coeff);
Cond_A=cond(A_coeff);
Sol_real=A_coeffb_coeff;
Error=A_coeff*Sol_real-b_coeff;
max(abs(Error)); linear equations, equation, system MATLAB Answers — New Questions

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