Help with applying the least squares method for solving simultaneous equations

Click For Summary
SUMMARY

The discussion focuses on applying the least squares method to solve a system of three simultaneous equations with three unknowns: Cx, Cy, and Cz. The equations are derived from experimentally measured data, which introduces variability that prevents the use of Reduced Row Echelon Form (RREF) for a unique solution. Yasith asserts that with three equations and three unknowns, a unique solution exists unless redundancy is present, challenging the need for an approximate solution due to experimental error.

PREREQUISITES
  • Understanding of simultaneous equations and their solutions
  • Familiarity with the least squares method
  • Knowledge of experimental data handling and error analysis
  • Basic proficiency in linear algebra concepts
NEXT STEPS
  • Study the least squares method for solving overdetermined systems
  • Learn about error propagation in experimental data
  • Explore techniques for identifying redundancy in systems of equations
  • Investigate numerical methods for approximating solutions in linear algebra
USEFUL FOR

Researchers, engineers, and data analysts dealing with experimental data who need to solve systems of equations while accounting for measurement errors.

yasith
Messages
14
Reaction score
0
Hi everyone given the system of equations

A1Cx + B1Cy + C1Cz = D1
A2Cx + B2Cy + C2Cz = D2
A3Cx + B3Cy + C3Cz = D3

I need to solve for Cx, Cy, Cz
All other variables are known and constants.
However all other variables (A,b,c,d) come from experimentally measured data and thus I cannot use RREF to derive a unique solution.

This system will only have an approximate solution. Please help me with the strategy for solving these equations.

Yasith
 
Physics news on Phys.org
You have 3 equations and 3 unknowns. In the absence of any further information, and assuming there's no redundancy in the set of equations, there will be a unique, exact solution. I see no basis for allowing for experimental error.
If you had more equations then there's a standard technique, and it sounds like you're aware of that.
 

Similar threads

Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Nonlinear Least Squares or OLS for Nonlinear Models?
  • · Replies 7 ·
Replies
7
Views
3K
Graduate Substitution to turn a non-linear least squares problem into a linear one
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad PDEs: Laplace's Equation over a Parallelogram
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad On the approximate solution obtained through Euler's method
  • · Replies 1 ·
Replies
1
Views
4K
MHB Least squares method : approximation of a cubic polynomial
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Linear least-squares method and row multiplication of matrix
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Linear least squares regression for model matrix identification
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Is it possible to solve such a differential equation?
  • · Replies 20 ·
Replies
20
Views
3K
Exponential Least Squares Method
  • · Replies 12 ·
Replies
12
Views
4K