The dual inverse scaling and squaring algorithm for the matrix logarithm

Abstract The inverse scaling and squaring algorithm computes the logarithm of a square matrix $A$ by evaluating rational approximant to at $B:=A^{2^{-s}}$ for suitable choice $s$. We introduce dual approach approximate $B$ solving equation $r(X)=B$, where $r$ is diagonal Padé exponential $0$. This solved substitution technique in style those developed Fasi & Iannazzo (2020, Substitution algorithms equations. Elect. Trans. Num. Anal., 53, 500–521). new method tailored special structure approximants terms computational cost more efficient than state-of-the-art algorithm.