In this paper a theorem is proven thatthe contribution of any linear circuit elements to theadmittance matrix [Y] in the modified nodal admit-tance (MNA) equation of circuit analysis is invariantwith time.Based on this theorem a fast time-domainalgorithm of partial matrix elimination (PME) is de-veloped for simulation of high-speed nonlinear circuitswith interconnects.In PME the matrix [Y] is ar-ranged to consist of two submatrices.The lower sub-matrix that contains entries from only linear circuit el-ements is partially triangulated by Gauss eliminationfor the first-time-step transient analysis.At the fol-lowing time steps of transient analysis,Gauss elimina-tion is needed only for the upper submatrix containingcontributions of nonlinear circuit devices.Efficiencyanalysis of PME is given in detail,showing that it canaccelerate circuit simulation by a factor of at least 2.5for linear or lightly nonlinear circuits without employ-ing any numerical approximation.Moreover,PME isuseful for circuits debugging.