Generalized conjugate systems on local fields

Local Functionals and Generalized Random Fields

On X ̃-frames and conjugate systems in Banach spaces

The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an $tilde{X}$-frame and a system conjugate to $tilde{X}$-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of $tilde{X}$-frame having a conjugate system is studied.

On nonlinear generalized conjugate gradient methods

where F (ξ) is a nonlinear operator from a real Euclidean space of dimension n or Hilbert space into itself. The Euclidean norm and corresponding inner product will be denoted by ‖·‖1 and (·, ·)1 respectively. A general different inner product with a weight function and the corresponding norm will be denoted by (·, ·)0 and ‖ · ‖ respectively. In the first part of this article (Sects. 2 and 3) w...

Generalized conjugate gradient squared

The Conjugate Gradient Squared (CGS) is an iterative method for solving nonsymmetric linear systems of equations. However, during the iteration large residual norms may appear, which may lead to inaccurate approximate solutions or may even deteriorate the convergence rate. Instead of squaring the Bi-CG polynomial as in CGS, we propose to consider products of two nearby Bi-CG polynomials which l...

Generalized Conjugate Gradient Squareddiederik

The Conjugate Gradient Squared (CGS) is a well-known and widely used iterative method for solving non-symmetric linear systems of equations. In practice the method converges fast, often twice as fast as the Bi-Conjugate Gradient (Bi-CG) method. However, during the iteration large residual norms may appear, which may lead to inaccurate approximate solutions or may even deteriorate the convergenc...