Real Symmetric Numerical Diagonalization of Third-Order Systems

The precision is fixed at 0.1^6.
For the off-diagonal elements above the diagonal, convergence is determined when the element with the largest absolute value
is within the specified precision.
The maximum number of loop iterations is fixed at 100.
Even if convergence is not achieved, the iterative process will terminate after the maximum number of iterations.
The program uses the off-diagonal elements above the diagonal of the input matrix to overwrite the lower elements,
converts the matrix to a symmetric form, and then begins processing. The input fields for the lower elements
are provided solely for better readability.
Only the diagonal elements and those above the diagonal are used as input values.
Please note whether the “E-?” format—which uses an exponent to represent small numbers—appears to the right of the output field.
The larger the “?”, the closer the result in the output field is to 0.
The diagonal elements are numerically calculated eigenvalues, but their positions along the diagonal may change
depending on factors such as the number of loop iterations.