Solving systems of algebraic linear equations is among the most frequent problems in
scientific computing. It appears in many areas like physics, engineering, chemistry, biology …

Breakdown in Lanczos-type algorithms is a common phenomenon which is due to the non-
existence of some orthogonal polynomials. It causes the solution process to halt. It is …

Lanczos-type algorithms are well known for their inherent instability. They typically
breakdown occurs when relevant orthogonal polynomials do not exist. Current approaches …

Lanczos methods for solving $\textit {A}\textbf {x}=\textbf {b} $ consist in constructing a
sequence of vectors $(\textbf {x} _k), k= 1,... $ such that $\textbf {r} _ {k}=\textbf {b}-\textit …

Lanczos-type algorithms are well known for their inherent instability. They typically
breakdown when relevant orthogonal polynomials do not exist. Current approaches to …

Modified embedding interpolation and extrapolation model in Lanczos-types algorithms
(MEIEMLA) is well-nown as a strategy to avoid brea down in Lanczos-type algorithms by ta …

Lanczos-type algorithms are mostly derived using recurrence relationships between formal
orthogonal polynomials. Various recurrence relations between these polynomials can be …

Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown
frequently and well before convergence has been achieved. These algorithms are typically …

Various recurrence relations between formal orthogonal polynomials can be used to derive
Lanczos-type algorithms. In this paper, we consider recurrence relation $ A_ {12} $ for the …

There are numerous algorithms for the solution of systems of linear equations and
eigenvalue problems. Among such methods, one of the best known iterative schemes is the …