Improvements in transaural synthesis with the Moore-Penrose pseudoinverse matrix

2018 ◽  
Vol 143 (3) ◽  
pp. 1938-1938 ◽  
Author(s):  
Aimee Shore ◽  
William M. Hartmann
Keyword(s):  
Pseudoinverse Matrix ◽  
Penrose Pseudoinverse

scholarly journals Stress Field Gradient Analysis Technique Using Lower-OrderC0Elements

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Jianwei Xing ◽  
Gangtie Zheng
Keyword(s):  
Stress Field ◽  
Lower Order ◽  
Gradient Analysis ◽  
Stress Gradient ◽  
Mathematical Technique ◽  
Element Analysis ◽  
Analysis Technique ◽  
Penrose Pseudoinverse ◽  
Element Type ◽  
Inconsistent Equation

For evaluating the stress gradient, a mathematical technique based on the stress field of lower-orderC0elements is developed in this paper. With nodal stress results and location information, an overdetermined and inconsistent equation of stress gradient is established and the minimum norm least squares solution is obtained by the Moore-Penrose pseudoinverse. This technique can be applied to any element type in comparison with the superconvergent patch (SCP) recovery for the stress gradient, which requires the quadratic elements at least and has to invert the Jacobi and Hessian matrices. The accuracy and validity of the presented method are demonstrated by two examples, especially its merit of achieving high accuracy with lower-order linearC0elements. This method can be conveniently introduced into the general finite element analysis programs as a postprocessing module.

scholarly journals On Moore-Penrose Pseudoinverse Computation for Stiffness Matrices Resulting from Higher Order Approximation

2019 ◽  
Vol 2019 ◽  
pp. 1-16
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Numerical Modeling ◽  
Computational Methods ◽  
Order Approximation ◽  
Higher Order ◽  
Benchmark Test ◽  
Essential Component ◽  
Stiffness Matrices ◽  
Penrose Pseudoinverse

Computing the pseudoinverse of a matrix is an essential component of many computational methods. It arises in statistics, graphics, robotics, numerical modeling, and many more areas. Therefore, it is desirable to select reliable algorithms that can perform this operation efficiently and robustly. A demanding benchmark test for the pseudoinverse computation was introduced. The stiffness matrices for higher order approximation turned out to be such tough problems and therefore can serve as good benchmarks for algorithms of the pseudoinverse computation. It was found out that only one algorithm, out of five known from literature, enabled us to obtain acceptable results for the pseudoinverse of the proposed benchmark test.

scholarly journals Improved Qrginv Algorithm for Computing Moore-Penrose Inverse Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Alireza Ataei
Keyword(s):  
Numerical Experiments ◽  
Computation Time ◽  
Computational Method ◽  
Real Matrix ◽  
Pseudoinverse Matrix ◽  
Arbitrary Matrix ◽  
Pseudo Inverse

Katsikis et al. presented a computational method in order to calculate the Moore-Penrose inverse of an arbitrary matrix (including singular and rectangular) (2011). In this paper, an improved version of this method is presented for computing the pseudo inverse of an m×n real matrix A with rank r>0. Numerical experiments show that the resulting pseudoinverse matrix is reasonably accurate and its computation time is significantly less than that obtained by Katsikis et al.

Cryptanalysis of schemes based on pseudoinverse matrix

2016 ◽  
Vol 21 (3) ◽  
pp. 209-213
Author(s):  
Jinhui Liu ◽  
Huanguo Zhang ◽  
Jianwei Jia
Keyword(s):  
Pseudoinverse Matrix

scholarly journals Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem

2003 ◽  
Vol 2003 (9) ◽  
pp. 459-485
Author(s):  
Brian J. McCartin
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Symmetric Matrix ◽  
Comprehensive Treatment ◽  
Matrix Eigenvalue Problem ◽  
Degenerate Problem ◽  
Matrix Eigenvalue ◽  
Penrose Pseudoinverse ◽  
Schrödinger Perturbation

A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example.

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