6 citations · 15 across the 5 of their papers we have counts for
5 papers
Matrix majorization in large samples
Muhammad Usman Farooq, Tobias Fritz, Erkka Haapasalo +1
One tuple of probability vectors is more informative than another tuple when there exists a single stochastic matrix transforming the probability vectors of the first tuple into th…
A new Lanczos type algorithm for system of linear equations
Muhammad Farooq, Abdellah Salhi
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically b…
A Switching Approach to Avoid Breakdown in Lanczos-type Algorithms
Muhammad Farooq, Abdellah Salhi
Lanczos-type algorithms are well known for their inherent instability. They typically breakdown when relevant orthogonal polynomials do not exist. Current approaches to avoiding br…
An alternative derivation of a new Lanczos-type algorithm for systems of linear equations
Saif Ullah, Muhammad Farooq, Abdellah Salhi
Various recurrence relations between formal orthogonal polynomials can be used to derive Lanczos-type algorithms. In this paper, we consider recurrence relation for the ch…
New Recurrence Relationships between Orthogonal Polynomials which Lead to New Lanczos-type Algorithms
Muhammad Farooq, Abdellah Salhi
Lanczos methods for solving consist in constructing a sequence of vectors such that $\textbf{r}_{k}=\textbf{b}-\textit{A…