We develop numerically stable and accurate stochastic simulation approaches for solving dynamic economic models. First, instead of standard least-squares approximation methods, we examine a variety of alternatives, including leastsquares methods using singular value decomposition and Tikhonov regularization, least-absolute deviations methods, and principal component regression method, all of wh...

Inferring dynamics of metabolic networks directly from metabolomics data provides a promising way to elucidate the underlying mechanisms of biological systems, as reported in our previous studies (Weckwerth, 2011; Sun and Weckwerth, 2012; Nägele et al., 2014) by a differential Jacobian approach. The Jacobian is solved from an overdetermined system of equations as JC + CJ(T)  = -2D, called Lyapu...

This special issue of Advances in Computational Mathematics is devoted to Numerical and Applied Linear Algebra, which is an important area of mathematics and a fundamental part of engineering and computational science problems. One of the main tools of this area is matrices, properties of which are studied and computations of them are performed, with different methods, in a variety of applicati...

Several U.S. Nuclear Power Plants are attempting to move from a periodic sensor calibration schedule to a condition-based schedule using on-line calibration monitoring systems. This move requires a license amendment that must address the requirements set forth in a recently released Nuclear Regulatory Commission Safety Evaluation Report (SER). The major issue addressed in the SER is that of a c...

A version of the Dynamic Systems Method for solving ill-conditioned linear algebraic systems is studied in this paper. An a priori and a posteriori stopping rules are justified. Algorithms for computing the solution in the case when SVD of the lefthand side matrix is available is presented. Numerical results show that when SVD of the left-hand side matrix is available or not computationally exp...

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. We present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, we outline an automatic adaptive refinement algorithm that minimizes the spatial discretization error in the transfer matrix,...

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. We present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, we outline an automatic adaptive reenement algorithm that minimizes the spatial discretization error in the transfer matrix, ...

One of the fundamental problems in theoretical electrocardiography can be characterized by an inverse problem. We present new methods for achieving better estimates of heart surface potential distributions in terms of torso potentials through an inverse procedure. First, we outline an automatic adaptive refinement algorithm that minimizes the spatial discretization error in the transfer matrix ...

Truncated Singular Value Decomposition (SVD) calculates the closest rank-k approximation of a given input matrix. Selecting the appropriate rank k defines a critical model order choice in most applications of SVD. To obtain a principled cut-off criterion for the spectrum, we convert the underlying optimization problem into a noisy channel coding problem. The optimal approximation capacity of th...

PURPOSE To develop a new shimming calculation method, which can calculate iron piece placements rapidly to make the magnetic field homogeneous at intended homogeneity and then to make the shimming working time short. MATERIALS AND METHODS The shimming calculation yields magnetic moment (MM) distribution, which is calculated by the truncated singular value decomposition (SVD) from the measured...