On the choice of the residual norm function in the interpretation of ARXPS data by regularized fitting

2010 ◽  
Vol 42 (3) ◽  
pp. 117-122
Author(s):  
R. W. Paynter ◽  
M. Rondeau
Keyword(s):  
Residual Norm

scholarly journals Magnetic induction pneumography: a planar coil system for continuous monitoring of lung function via contactless measurements

2019 ◽  
Vol 1 (1) ◽  
pp. 56-62 ◽  
Author(s):  
Doğa Gürsoy ◽  
Hermann Scharfetter
Keyword(s):  
Lung Function ◽  
Magnetic Induction ◽  
Continuous Monitoring ◽  
Patient Comfort ◽  
Point Spread Functions ◽  
Mechanically Ventilated ◽  
Planar Coil ◽  
Residual Norm ◽  
Imaging Artifacts ◽  
Internal Conductivity

Abstract Continuous monitoring of lung function is of particular interest to the mechanically ventilated patients during critical care. Recent studies have shown that magnetic induction measurements with single coils provide signals which are correlated with the lung dynamics and this idea is extended here by using a 5 by 5 planar coil matrix for data acquisition in order to image the regional thoracic conductivity changes. The coil matrix can easily be mounted onto the patient bed, and thus, the problems faced in methods that use contacting sensors can readily be eliminated and the patient comfort can be improved. In the proposed technique, the data are acquired by successively exciting each coil in order to induce an eddy-current density within the dorsal tissues and measuring the corresponding response magnetic field strength by the remaining coils. The recorded set of data is then used to reconstruct the internal conductivity distribution by means of algorithms that minimize the residual norm between the estimated and measured data. To investigate the feasibility of the technique, the sensitivity maps and the point spread functions at different locations and depths were studied. To simulate a realistic scenario, a chest model was generated by segmenting the tissue boundaries from NMR images. The reconstructions of the ventilation distribution and the development of an edematous lung injury were presented. The imaging artifacts caused by either the incorrect positioning of the patient or the expansion of the chest wall due to breathing were illustrated by simulations.

scholarly journals Usage of the convergence test of the residual norm in the Tsuno-Nodera version of the GMRES algorithm

2007 ◽  
Vol 49 (2) ◽  
pp. 293-308
Author(s):  
K. Moriya ◽  
T. Nodera
Keyword(s):  
Distribution Of Zeros ◽  
Numerical Examples ◽  
Convergence Test ◽  
New Variant ◽  
Residual Norm ◽  
Gmres Algorithm

AbstractTsuno and Nodera proposed a new variant of the GMRES(m) algorithm. Their algorithm is referred to as the GMRES(≤ mmax) algorithm and performs the restart process adaptively, considering the distribution of the zeros of the residual polynomial. However, unless the zeros of the residual polynomial are distributed uniformly, mass is always chosen and their algorithm becomes almost the same as the GMRES(m) algorithm with m = mmax. In this paper, we include a convergence test for the residual norm in the GMRES(≤ mmax) algorithm and propose a new restarting technique based on two criteria. Even if the distribution of zeros does not become uniform, the restart can be performed by using the convergence test of the residual norm. Numerical examples simulated on a Compaq Beowulf computer demonstrate that the proposed technique accelerates the convergence of the GMRES(≤ mmax) algorithm.

NONLINEAR APPROACH TO APPROXIMATE ACOUSTIC BOUNDARY ADMITTANCE IN CAVITIES

2007 ◽  
Vol 15 (01) ◽  
pp. 63-79 ◽  
Author(s):  
ROBERT ANDERSSOHN ◽  
STEFFEN MARBURG
Keyword(s):  
Boundary Condition ◽  
Sound Pressure ◽  
Pressure Field ◽  
Initial Boundary ◽  
System Matrix ◽  
Forward Solution ◽  
Piecewise Constant ◽  
Direct Inversion ◽  
Nonlinear Approach ◽  
Residual Norm

In this paper, an algorithm is derived to solve a problem of inverse acoustics. It considers the damped acoustic boundary value problem, i.e. the Helmholtz equation and admittance boundary condition, in order to approximate the boundary admittance of interior domains. The algorithm is implemented by using a finite element method and tested for two-dimensional cavities with arbitrary shapes. The admittance condition is reconstructed based on sound pressure measurements. The solution of the arising nonlinear system of equations is obtained by applying the Newton method following a presetting method for finding reasonable initial boundary admittance values. A residual norm accounts for the objective function. Its first- and second-order sensitivities are determined analytically by using a modal decomposition in order to avoid direct inversion of the system matrix. The experiment is simulated by taking sound pressure data of the forward solution as inputs for the inverse problem. Test examples show that very few measurement points are necessary to reproduce piecewise constant boundary admittance values very accurately. Then, the admittance boundary condition is applied to reproduce the sound pressure distribution in the cavity. Again, it becomes obvious that only a few measurement points are required to reconstruct the sound pressure field.

scholarly journals Numerical techniques for behavior of incompressible flow in steady two-dimensional motion due to a linearly stretching of porous sheet based on radial basis functions

2019 ◽  
Vol 8 (1) ◽  
pp. 80-93
Author(s):  
Kourosh Parand ◽  
Yasaman Lotfi ◽  
Jamal Amani Rad
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
High Rate ◽  
Algebraic Equations ◽  
Polar Fluid ◽  
Radial Basis ◽  
Residual Norm ◽  
Layer Flow ◽  
Non Linear System ◽  
Better Than

AbstractIn this paper the boundary layer flow of a micro-polar fluid due to a linearly stretching sheet which is a non-linear system two-point boundary value problem (BVP) on semi-infinite interval has been considered. This the sheets are included the suction and injection. We solve this problem by two different collecation approaches and compare their results with solution of other methods. The proposed approaches are equipped by the direct (DRBF) and indirect radial basis functions (IRBF). Direct approach (DRBF) is based on a differential process and indirect approach (IRBF) is based on an integration process. These methods reduce solution of the problem to solution of a system of algebraic equations. Numerical results and residual norm show that the IRBF performs better than the common DRBF, and has an acceptable accuracy and high rate of convergence of IRBF process.

On the Residual Norm in FOM and GMRES

2011 ◽  
Vol 32 (2) ◽  
pp. 394-411 ◽  
Author(s):  
Gérard Meurant
Keyword(s):  
Residual Norm

scholarly journals Improvement of preconditioned bi-Lanczos-type algorithms with residual norm minimization for the stable solution of systems of linear equations

2021 ◽  
Author(s):  
Shoji Itoh
Keyword(s):  
Relative Error ◽  
Conjugate Gradient ◽  
Linear Equations ◽  
Stable Solution ◽  
Stopping Criterion ◽  
Type Method ◽  
Stabilized Method ◽  
Norm Minimization ◽  
Systems Of Linear Equations ◽  
Residual Norm

AbstractIn this paper, improved algorithms are proposed for preconditioned bi-Lanczos-type methods with residual norm minimization for the stable solution of systems of linear equations. In particular, preconditioned algorithms pertaining to the bi-conjugate gradient stabilized method (BiCGStab) and the generalized product-type method based on the BiCG (GPBiCG) have been improved. These algorithms are more stable compared to conventional alternatives. Further, a stopping criterion changeover is proposed for use with these improved algorithms. This results in higher accuracy (lower true relative error) compared to the case where no changeover is done. Numerical results confirm the improvements with respect to the preconditioned BiCGStab, the preconditioned GPBiCG, and stopping criterion changeover. These improvements could potentially be applied to other preconditioned algorithms based on bi-Lanczos-type methods.

scholarly journals Solving the Nonlinear Heat Equilibrium Problems Using the Local Multiquadric Radial Basis Function Collocation Method

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1289 ◽  
Author(s):  
Weichung Yeih
Keyword(s):  
Radial Basis Function ◽  
Collocation Method ◽  
Basis Function ◽  
Equilibrium Problems ◽  
Collocation Point ◽  
Absolute Error ◽  
Algebraic Equations ◽  
Radial Basis ◽  
Residual Norm

In this article, the nonlinear heat equilibrium problems are solved by the local multiquadric (MQ) radial basis function (RBF) collocation method. The system of nonlinear algebraic equations is solved by iteration based on the residual norm-based algorithm, in which the direction of evolution is determined by a linear equation. In addition, the role of the collocation point and source point is clearly defined such that in our proposed method the field value of any interested point can be expressed. Six numerical examples are shown to check the performance of the proposed method. As the number of supporting points (mp) increases, the accuracy of numerical solution increases. Among all examples, mp = 50 can perform well. In addition, the selection of shape parameter, c, affects the accuracy. However, as c < 2 the maximum relative absolute error percentage is less than 1%.

scholarly journals Augmented Tikhonov Regularization Method for Dynamic Load Identification

2020 ◽  
Vol 10 (18) ◽  
pp. 6348 ◽  
Author(s):  
Jinhui Jiang ◽  
Hongzhi Tang ◽  
M Shadi Mohamed ◽  
Shuyi Luo ◽  
Jianding Chen
Keyword(s):  
Kernel Function ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Identification Accuracy ◽  
Tikhonov Regularization Method ◽  
Load Identification ◽  
Structural Dynamic ◽  
Green Kernel ◽  
Ill Posed ◽  
Residual Norm

We introduce the augmented Tikhonov regularization method motivated by Bayesian principle to improve the load identification accuracy in seriously ill-posed problems. Firstly, the Green kernel function of a structural dynamic response is established; then, the unknown external loads are identified. In order to reduce the identification error, the augmented Tikhonov regularization method is combined with the Green kernel function. It should be also noted that we propose a novel algorithm to determine the initial values of the regularization parameters. The initial value is selected by finding a local minimum value of the slope of the residual norm. To verify the effectiveness and the accuracy of the proposed method, three experiments are performed, and then the proposed algorithm is used to reproduce the experimental results numerically. Numerical comparisons with the standard Tikhonov regularization method show the advantages of the proposed method. Furthermore, the presented results show clear advantages when dealing with ill-posedness of the problem.

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