  In-memory computing with crosspoint resistive memory arrays has gained
enormous attention to accelerate the matrix-vector multiplication in the
computation of data-centric applications. By combining a crosspoint array and
feedback amplifiers, it is possible to compute matrix eigenvectors in one step
without algorithmic iterations. In this work, time complexity of the
eigenvector computation is investigated, based on the feedback analysis of the
crosspoint circuit. The results show that the computing time of the circuit is
determined by the mismatch degree of the eigenvalues implemented in the
circuit, which controls the rising speed of output voltages. For a dataset of
random matrices, the time for computing the dominant eigenvector in the circuit
is constant for various matrix sizes, namely the time complexity is O(1). The
O(1) time complexity is also supported by simulations of PageRank of real-world
datasets. This work paves the way for fast, energy-efficient accelerators for
eigenvector computation in a wide range of practical applications.
