Abstract: In this pedagogical article, I explore a unified approach in obtaining the derivatives of functions and their inverses by adopting a guided self-discovery approach. I begin by finding the ...

For an inner function θ on the upper half-plane ℂ+, we look at the star-invariant subspace ${\mathrm{K}}_{0}^{\mathrm{p}}:={\mathrm{H}}^{\mathrm{p}}\cap \mathrm ...

Applications of Fréchet derivative emerge in the sensitivity analysis of matrix functions. Our work extends the generalized complex step approximation using the complex computation f(A + eiθhE) as a ...