Faster stochastic trace estimation with a Chebyshev product identity

Methods for stochastic trace estimation often require the repeated evaluation of expressions form zTpn(A)z, where A is a symmetric matrix and pn degree n polynomial written in standard or Chebyshev basis. We show how to evaluate these using only ⌈n∕2⌉ matrix–vector products, thus substantially reducing cost existing algorithms that use interpolation Taylor series.