Unitary orthogonalization processes
Let \({\mathcal H}\) be a complex separable Hilbert space over \(\mathbb{C}\) with an inner product \((.,.)\), \(U:{\mathcal H}\to {\mathcal H}\) be a unitary operator (i.e. \((Ux,Uy)= (x, y)\) for all \(x,y\in {\mathcal H}\)) and \(0\neq h\in{\mathcal H}\). The authors consider a two-sided orthogonalization process for the bilateral Krylov sequence \(\{U^kh\}^\infty_{k=-\infty}\), which is equivalent to the Gragg's isometric Arnoldi process. The connection of this process to other classical algorithms of signal processing is also discussed.
scientific article; zbMATH DE number 1115941
scientific article