Newton's iteration for inversion of Cauchy-like and other structured matrices
The authors consider the solution of a nonsingular Cauchy-like linear system, \(Cx=v\), and the inversion of a nonsingular Cauchy-like matrix \(C\). They modify the Newton iterations in a way which leads to a significant saving of the computational time and memory space. The algorithm can also be extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices.
scientific article; zbMATH DE number 1040689
scientific article