In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer ...

Dr. James McCaffrey of Microsoft Research presents a full-code, step-by-step tutorial on an implementation of the technique that emphasizes simplicity and ease-of-modification over robustness and ...

Drazin inverses and their modern generalisations constitute a pivotal area of operator theory within Banach algebras. These inverse concepts extend the classic notion of the matrix inverse to settings ...

In this paper, we analyze the index relation of anti-triangular block matrices and their entries to separately obtain new and strict expressions for the Drazin inverse of them under certain ...

Dr. James McCaffrey from Microsoft Research presents a complete end-to-end demonstration of computing a matrix inverse using the Newton iteration algorithm. Compared to other algorithms, Newton ...