A crucial problem concerning Tikhonov regularization is the proper choice of the regularization parameter. This paper deals with a generalization of a parameter choice rule due to Regińska (1996) [31], analyzed and algorithmically realized through a fast fixed-point method in Bazán (2008) [3], which results in a fixed-point method for multi-parameter Tikhonov regularization called MFP. Like the...

one of the most remarkable basis of the gravity data inversion is the recognition of sharp boundaries between an ore body and its host rocks during the interpretation step. therefore, in this work, it is attempted to develop an inversion approach to determine a 3d density distribution that produces a given gravity anomaly. the subsurface model consists of a 3d rectangular prisms of known sizes ...

In this paper we propose a variant of the Rayleigh quotient method to compute an eigenvalue and corresponding eigenvectors of a matrix. It is based on the observation that eigenvectors of a matrix with eigenvalue zero are also singular vectors corresponding to zero singular values. Instead of computing eigenvector approximations by the inverse power method, we take them to be the singular vecto...

s 6 Awad H. Al-Mohy An Improved Algorithm for the Matrix Logarithm . . . . . . . . . . . . . . . . . . . . 7 David Amsallem Interpolation on Matrix Manifolds of Reduced-Order Models and Application to On-Line Aeroelastic Predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Athanasios C. Antoulas Model Reduction of Parameter-Dependent Systems . . . . . . . . . . . . . . . . . . ...

This paper presents new implementation of one–sided Jacobi SVD for triangular matrices and its use as the core routine in a new preconditioned Jacobi SVD algorithm, recently proposed by the authors. New pivot strategy exploits the triangular form and uses the fact that the input triangular matrix is the result of rank revealing QR factorization. If used in the preconditioned Jacobi SVD algorith...

This paper presents new implementation of one–sided Jacobi SVD for triangular matrices and its use as the core routine in a new preconditioned Jacobi SVD algorithm, recently proposed by the authors. New pivot strategy exploits the triangular form and uses the fact that the input triangular matrix is the result of rank revealing QR factorization. If used in the preconditioned Jacobi SVD algorith...

We study and analyze a nonmonotone globally convergent method for minimization on closed sets. This method is based on the ideas from trust-region and Levenberg-Marquardt methods. Thus, the subproblems consists in minimizing a quadratic model of the objective function subject to a given constraint set. We incorporate concepts of bidiagonalization and calculation of the SVD “with inaccuracy” to ...

In the robot navigation problem, noisy sensor data must be ltered to obtain the best estimate of the robot position. The discrete Kalman lter, which usually is used for prediction and detection of signal in communication and control problems has become a commonly used method to reduce the e ect of uncertainty from the sensor data. However, due to the special domain of robot navigation, the Kalm...

Tikhonov regularization of linear discrete ill-posed problems often is applied with a finite difference regularization operator that approximates a low-order derivative. These operators generally are represented by banded rectangular matrices with fewer rows than columns. They therefore cannot be applied in iterative methods that are based on the Arnoldi process, which requires the regularizati...

The total least squares (TLS) method is a successful method for noise reduction in linear least squares problems in a number of applications. The TLS method is suited to problems in which both the coefficient matrix and the right-hand side are not precisely known. This paper focuses on the use of TLS for solving problems with very ill-conditioned coefficient matrices whose singular values decay...