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Table 3 Condition number of the matrix \(\mathbf {W}_{\mathrm {t}}\hat {\mathbf {H}}_{\mathrm {t}}\) (\(L^{\mathrm {t}}_{g} = 1947\)) and of two sub-matrices \(\mathbf {W}_{\mathrm {s}}\hat {\mathbf {H}}_{\mathrm {s}}\) (\(L^{\mathrm {s}}_{g} = 1000\) and \(L^{\mathrm {s}}_{g} = 300\)) for PMINT

From: Improving the conditioning of the optimization criterion in acoustic multi-channel equalization using shorter reshaping filters

Filter length

Condition number

\(L^{\mathrm {t}}_{g} = 1947\)

\(\chi _{\mathbf {W}_{\mathrm {t}}\hat {\mathbf {H}}_{\mathrm {t}}} = 1.65 \times 10^{7}\)

\(L^{\mathrm {s}}_{g} = 1000\)

\(\chi _{\mathbf {W}_{\mathrm {s}}\hat {\mathbf {H}}_{\mathrm {s}}} = 4.91 \times 10^{3}\)

\(L^{\mathrm {s}}_{g} = 300\)

\(\chi _{\mathbf {W}_{\mathrm {s}}\hat {\mathbf {H}}_{\mathrm {s}}} = 6.23 \times 10^{2}\)

  1. The considered acoustic system is system S1 described in Section 6.1