For DSC, the Double Sum Combination we have an interaction between the different modes. The interaction is defined by the so-called correlation matrix [ ρg ] which now has also off-diagonal terms.
Rtot = √ ΣΣ RiT ρg Ri, for j=1 to n, and for i=1 to n
The idea for getting relevant concomitant values is to decompose the correlation matrix and to transform the equation such that it can later be treated like SRSS. We decompose [ρ] into 2 parts: [ρ] = [a]T*[a] and calculate the modified result matrix [Rm] = [a]* [R]. Then we apply the standard SRSS procedure to this modified matrix as described above.
For the decomposition of the matrix [ρ] we use currently a Cholesky procedure. However, the question is still disputed, whether the nature of the matrix [ρ] guarantees, that the decomposition in the real space is possible. In fact, we have noticed that in rare cases (considering many modes over a wide frequency range and/or mode-dependent damping with largely varying damping ratios) the Cholesky decomposition fails due to negative pivots arising in the calculation process.