The discussion resulted in a single equation to determine a coefficient vector which minimizes the cost function.

In order to generate the coefficient vector we are interested in the inverse of the deterministic autocorrelation matrix.

The coefficient matrix B is a matrix where the coefficient vectors for each regression problem are stacked horizontally:

Consider a speech signal , which can be represented in a domain such that , where speech signal , dictionary matrix and the sparse coefficient vector .

To achieve this goal, the idea is to limit the coefficient vector to a special subset , which satisfies below two conditions:

In this sense, the Lebesgue constant can be viewed as the relative condition number of the operator mapping each coefficient vector to the set of the values of the polynomial with coefficients in the Lagrange form.

One way to see this is to note that if we add a constant vector to all of the coefficient vectors, the equations are identical:

This means that, just as in the log-linear model, only K-1 of the coefficient vectors are identifiable, and the last one can be set to an arbitrary value (e.g. 0).

However every real nonnegative form can be approximated as closely as desired (in the -norm of its coefficient vector) by a sequence of forms that are SOS.

The ordinary least squares solution is to estimate the coefficient vector using the Moore-Penrose pseudoinverse: