Extracting the inductance of complex interconnect topologiesis a formidable task, and simulating the resulting dense partialinductance matrix is even more difficult. Furthermore, it is wellknown that simply discarding smallest terms to sparsify the inductancematrix can render the partial inductance matrix indefiniteand result in an unstable circuit model. In this paper, wedescribe a methodology for incrementally generating a sparsepartial inductance matrix based on using moments about s=0 todetermine when a sufficient number of mutual inductances havebeen captured. The minimally required mutual inductances areextracted for a provably stable model.