Approximating the Matrix Sign Function Using a Novel Iterative Method

Algorithm 1

The new method for computing the matrix sign.

(1) Given a suitable 𝑋₀∈ℂ^𝑛×𝑛

(2) for 𝑘=0,1,… until convergence do

(3)  𝐵_𝑘=𝐼+20𝑋²_𝑘+25𝑋⁴_𝑘+2𝑋⁶_𝑘

(4) Solve the linear system 𝐵_𝑘𝑋_𝑘+1=7𝑋_𝑘+30𝑋³_𝑘+11𝑋⁵_𝑘 for 𝑋_𝑘+1

(5) end for