Rob Haelterman

The Quasi-Newton Least Squares Method: A New and Fast Secant Method Analyzed for Linear Systems

We present a new quasi-Newton method that can solve systems of equations of which no information is known explicitly and which requires no special structure of the system matrix, like positive definiteness or sparseness. The method builds an approximate Jacobian based on input-output combinations of a black box system, uses a rank-one update of this Jacobian after each iteration, and satisfies the secant equation. While it has originally been developed for nonlinear equations we analyze its properties and performance when applied to linear systems. Analytically, the method is shown to be convergent in

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

n+1

Letter to the editor: On the non-singularity of the quasi-Newton-least squares method

iterations (

Equivalence of QN-LS and BQN-LS for affine problems

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Data fusion for improving thermal emissivity separation from hyperspectral data

being the number of unknowns), irrespective of the nature of the system matrix. The performance of this method is greatly superior to other quasi-Newton methods and comparable with GMRes when tested on a number of standardized test-cases.

On the similarities between the quasi-Newton least squares method and GMRes

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.

Short temporal change detection in complex urban area

We show that, for an affine problem, the approximate Jacobian of the Quasi-Newton-Least Squares method cannot become singular before the solution has been reached.

Multi-stage solvers optimized for damping and propagation

Previously, we studied methods to solve the coupled system of non-linear equations F ( g ) = p and S ( p ) = g . In this paper we take a closer look at two of them, the Quasi-Newton method with Least Squares Jacobian (QN-LS) and the Block Quasi-Newton method with Least Squares Jacobian (BQN-LS). We show that both are algebraically equivalent if one of the operators ( F or S ) is affine. This implies that for this type of problem there is no reason to use BQN-LS, as the results will be the same but for a higher computational cost.

A Comparison of Different Quasi-Newton Acceleration Methods for Partitioned Multi-Physics Codes

Land Surface Temperature (LST) and Land Surface Emissivity (LSE) are common retrievals from thermal hyperspectral imaging. However, their retrieval is not a straightforward procedure because the mathematical problem is ill-posed. This procedure becomes more challenging in an urban area where the spatial distribution of temperature varies substantially in space and time. In this study we propose a new method which integrates 3D surface information from LIDAR data in an attempt to improve the temperature and emissivity separation (TES) procedure for thermal hyperspectral scene. The experimental results prove the high accuracy of the proposed method in comparison to another conventional TES model.

Limited memory switched Broyden method for faster image deblurring

We show how the quasi-Newton least squares method (QN-LS) relates to Krylov subspace methods in general and to GMRes in particular.