NDLI: On the Similarities Between the Quasi-Newton Inverse Least Squares Method and GMRes

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Volume 47 Issue 6

Correction to Strict Diagonal Dominance and Optimal Bounds for the Skeel Condition Number

A Finite Element Method for Density Estimation with Gaussian Process Priors

Sharp Norm-Estimations for MoorePenrose Inverses of Stable Perturbations of Hilbert $C^*$-Module Operators

Quantization Based Filtering Method Using First Order Approximation

Compactness Properties of the DG and CG Time Stepping Schemes for Parabolic Equations

On the Similarities Between the Quasi-Newton Inverse Least Squares Method and GMRes

A Convergent Nonconforming Adaptive Finite Element Method with Quasi-Optimal Complexity

Local Error Estimates for SUPG Solutions of Advection-Dominated Elliptic Linear-Quadratic Optimal Control Problems

Block Monotone Iterative Method for Semilinear Parabolic Equations with Nonlinear Boundary Conditions

On the Strong Convergence of Gradients in Stabilized Degenerate Convex Minimization Problems

Spectral Analysis of DirichletNeumann Operators and Optimized Schwarz Methods with Robin Transmission Conditions

Analysis of a Quadratic Programming Decomposition Algorithm

Local Multilevel Methods for Adaptive Finite Element Methods for Nonsymmetric and Indefinite Elliptic Boundary Value Problems

Shear Locking in a Plane Elasticity Problem and the Enhanced Assumed Strain Method

A Posteriori Error Analysis of Finite Element Methods for ReissnerMindlin Plates

Error Estimates for a Finite Element Discretization of a Phase Field Model for Mixtures

Nonequispaced Hyperbolic Cross Fast Fourier Transform

On a General Class of Multipoint Root-Finding Methods of High Computational Efficiency

Error Estimate of Fourth-Order Compact Scheme for Linear Schrdinger Equations

Convergence Analysis of Planewave Expansion Methods for 2D Schrdinger Operators with Discontinuous Periodic Potentials

On the Fourier Extension of Nonperiodic Functions

High Order Contractive RungeKutta Methods for Volterra Functional Differential Equations

Multiscale Asymptotic Method for Maxwell's Equations in Composite Materials

Finite Element Approximations for StokesDarcy Flow with BeaversJoseph Interface Conditions

Robust BDDC Preconditioners for ReissnerMindlin Plate Bending Problems and MITC Elements

A Finite Volume Scheme for Diffusion Problems on General Meshes Applying Monotony Constraints

The Discrete Duality Finite Volume Method for Convection-diffusion Problems

A FETI-DP Formulation for the Stokes Problem without Primal Pressure Components

Fully Computable Error Bounds for Discontinuous Galerkin Finite Element Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes

Optimal Error Estimate for the Div Least-squares Method with Data $f\inL^2$ and Application to Nonlinear Problems

A Rational Interpolation Scheme with Superpolynomial Rate of Convergence

Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension

A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations

Volume 47 Issue 5

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Volume 47 Issue 2

Volume 47 Issue 1

On the Similarities Between the Quasi-Newton Inverse Least Squares Method and GMRes

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Vierendeels, Jan Van Heule, Dirk Haelterman, Rob Degroote, Joris
Copyright Year	2010
Abstract	We show how one of the best-known Krylov subspace methods, the generalized minimal residual method (GMRes), can be interpreted as a quasi-Newton method and how the quasi-Newton inverse least squares method (QN-ILS) relates to Krylov subspace methods in general and to GMRes in particular when applied to linear systems. We also show that we can modify QN-ILS in order to make it analytically equivalent to GMRes, without the need for extra matrix-vector products.
Starting Page	4660
Ending Page	4679
Page Count	20
File Format	PDF
ISSN	00361429
DOI	10.1137/090750354
e-ISSN	10957170
Issue Number	6
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-02-19
Access Restriction	Subscribed
Subject Keyword	Methods of quasi-Newton type Iterative methods for linear systems least squares quasi-Newton method rank-one update iterative method generalized minimal residual method linear algebra secant method Derivative-free methods and methods using generalized derivatives
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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