In this paper we compare various preconditioners for the numerical solution of partial differential equations. We compare the well-known balancing preconditioner used in domain decomposition methods with a so-called deflation preconditioner. We prove that the effective condition number of the deflated preconditioned system is always, i.e., for all deflation vectors and all restrictions and prol...

Modern treatments of structured Principal Component Analysis often focus on the estimation of a single component under various assumptions or priors, such as sparsity and smoothness, and then the procedure is extended to multiple components by sequential estimation interleaved with deflation. While prior work has highlighted the importance of proper deflation for ensuring the quality of the est...

5 Some Techniques to accelerate convergence in the QR algorithm 8 5.1 Deflation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.2 The Wilkinson shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.3 Obtaining the eigenvectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 5.4 Ad hoc shifts . . . . . . . . . . . . . . . . . . . . . . . . . . ...

The role played by both lung stretch and lung deflation components of the pulmonary vagus has been studied, in order to throw further light on the changes in lung mechanics which underlie the lung deflation receptor activity and hence the activation of respiration during an asthma attack. The discharge pattern of the lung stretch receptors varies from unit to unit, but also in one and the same ...

The C-method is an exact method for analyzing gratings and rough surfaces. This method leads to large-size dense complex non-Hermitian eigenvalue. In this paper, we introduce a parallel QR algorithm that is specifically designed for the C-method. We define the “early shift” for the matrix according to the observed properties. We propose a combination of the “early shift”, Wilkinson’s shift and ...

In analogy to the PCA setting, the sparse PCA problem is often solved by iteratively alternating between two subtasks: cardinality-constrained rank-one variance maximization and matrix deflation. While the former has received a great deal of attention in the literature, the latter is seldom analyzed and is typically borrowed without justification from the PCA context. In this work, we demonstra...

Life insurers are exposed to deflation risk: falling prices could lead to insufficient investment returns, and inflation-indexed protections could make insurers vulnerable to deflation. In this spirit, this paper proposes a market-based methodology for measuring deflation risk based on a discrete framework: the latter accounts for the real interest rate, the inflation index level, its condition...

Aggressive early deflation [1] has proven to significantly enhance the convergence of the QR algorithm for computing the eigenvalues of a nonsymmetric matrix. It is shown that this deflation strategy is equivalent to extracting converged Ritz vectors from certain Krylov subspaces. As a special case, the single-shift QR algorithm enhanced with aggressive early deflation corresponds to a Krylov s...

I will review recent developments in matrix deflation methods, by Ronald Morgan/Walter Wilcox, Andreas Stathopoulos/Konstantinos Orginos, and Martin Lüscher, with application to lattice QCD fermion inversion. I will begin with a short review of deflation-related work in the field. The Morgan/Wilcox algorithms using GMRES and BiCGStab for deflation will be described. Typical results for quenched...

In this paper oscillometric method is used to develop an adaptive non-invasive blood pressure measurement system. To overcome the drawback of conventional oscillometric method an algorithm is developed. During the time of deflation and inflation process the step size of pressure pumped and released using pump and valve respectively is varied adaptively by continuously monitoring the feedback wh...