so I just got 25 equations, there are 13 unknown parameters need to calculate for the lower case letters, it represment 13 unknown parameters that need to get, and for upper case letters, it represents 25 input values, what I want to similar to a=, b=,c=,d=,e=....

CodePudding user response：

Sorry, your image link isn't helpful.

Your equation looks like A*x = b. You have m equations and n unknowns to solve for. The matrix A is m x n; the vectors x and b are m x 1.

When m == n you can use LU decomposition to solve for the unknowns, as long as the matrix isn't singular.

When m > n you need a least squares fit.

When m < n you need Singular Value Decomposition.

Your "lower case/upper case" confuses me.

CodePudding user response：

Assuming this is linear system, you have an overconstrained system of equations. Since nobody is going to sit and transcribe your image, let's do a simple example.

Consider 3 equations with 2 unknowns

Which is organized as a linear system of equations as

To solve A x = b when rows(A) > size(x) use a least squares fit. This is done by pre-multiplying both sides by the transpose A^T

Then the system becomes solvable (A^T A) x = A^T b with solution

x = (A^T A)^-1 A^T b

in the example

or

which as you know is a solvable 2×2 system