TY - JOUR

T1 - Geometrical inverse matrix approximation for least-squares problems and acceleration strategies

AU - Chehab, Jean Paul

AU - Raydan, Marcos

N1 - CNRS (UMR CNRS 7352)
UID/MAT/00297/2019
Sem PDF conforme despacho.

PY - 2020

Y1 - 2020

N2 - We extend the geometrical inverse approximation approach to the linear least-squares scenario. For that, we focus on the minimization of 1 − cos (X(ATA) , I) , where A is a full-rank matrix of size m × n, with m ≥ n, and X is an approximation of the inverse of ATA. In particular, we adapt the recently published simplified gradient-type iterative scheme MinCos to the least-squares problem. In addition, we combine the generated convergent sequence of matrices with well-known acceleration strategies based on recently developed matrix extrapolation methods, and also with some line search acceleration schemes which are based on selecting an appropriate steplength at each iteration. A set of numerical experiments, including large-scale problems, are presented to illustrate the performance of the different accelerations strategies.

AB - We extend the geometrical inverse approximation approach to the linear least-squares scenario. For that, we focus on the minimization of 1 − cos (X(ATA) , I) , where A is a full-rank matrix of size m × n, with m ≥ n, and X is an approximation of the inverse of ATA. In particular, we adapt the recently published simplified gradient-type iterative scheme MinCos to the least-squares problem. In addition, we combine the generated convergent sequence of matrices with well-known acceleration strategies based on recently developed matrix extrapolation methods, and also with some line search acceleration schemes which are based on selecting an appropriate steplength at each iteration. A set of numerical experiments, including large-scale problems, are presented to illustrate the performance of the different accelerations strategies.

KW - Gradient-type methods

KW - Inverse approximation

KW - Matrix acceleration techniques

UR - http://www.scopus.com/inward/record.url?scp=85077618620&partnerID=8YFLogxK

U2 - 10.1007/s11075-019-00862-z

DO - 10.1007/s11075-019-00862-z

M3 - Article

AN - SCOPUS:85077618620

VL - 85

SP - 1213

EP - 1231

JO - Numerical Algorithms

JF - Numerical Algorithms

SN - 1017-1398

ER -