1. In a circuit simulation tool, a method for determining a periodic steady state response of a circuit driven by a periodic signal, the periodic signal being an input to the circuit, the method comprising the steps of: producing a first linear system of equations characterizing nodal voltages of said circuit; producing a second non-linear system of equations based on the first system of equations using a shooting method, the second non-linear system of equations representing initial conditions of the circuit that directly result in the periodic steady state response; solving the second non-linear system of equations using a Newton iterative method to produce the periodic steady state response of the circuit, including producing for each iteration of the Newton method a corresponding third linear system of equations based on the second non-linear system of equations; for each iteration of the Newton method, solving its corresponding third linear system of equations using a matrix-implicit iterative technique, including providing a plurality of matrices stored in a memory to contain coefficients relating to the third linear system of equations, each of the matrices having an identical structure, the structure indicating locations of non-zero elements in each of the matrices; wherein data representing the structure is stored in the memory only once, and for each of the matrices, data representing non-zero elements of the matrix are stored in the memory apart from the data representing the structure; and providing the periodic steady state response to the circuit simulation tool.