In this work, we carry out the convergence analysis of a positive DDFV method for approximating solutions of degenerate parabolic equations. The basic idea rests upon different approximations of the fluxes on the same interface of the control volume. Precisely, the approximated flux is split into two terms corresponding to the primal and dual normal components. Then the first term is discretized using

Recently, some matrix exponential-based discriminant analysis methods were proposed for high dimensionality reduction. It has been shown that they often have more discriminant power than the corresponding discriminant analysis methods. However, one has to solve some large-scale matrix exponential eigenvalue problems which constitutes the bottleneck in this type of methods. The main contribution of

Three new procedures for computation the scaling parameter in the self-scaling memoryless Broyden–Fletcher–Goldfarb–Shanno search direction with a parameter are presented. The first two are based on clustering the eigenvalues of the self-scaling memoryless Broyden–Fletcher–Goldfarb–Shanno iteration matrix with a parameter by using the determinant or the trace of this matrix. The third one is based

Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue problems. We present simple but efficient selection methods based on divided differences to do this. Selection means that the approximate eigenpair is picked from candidate

In this paper, we propose a new preconditioned SOR method for solving the multi-linear systems whose coefficient tensor is an \({\mathcal{M}}\)-tensor. The corresponding comparison for spectral radii of iterative tensors is given. Numerical examples demonstrate the efficiency of the proposed preconditioned methods.

In this paper, we modify the accelerated generalized successive overrelaxation (AGSOR) method for block two-by-two complex linear systems, and use the AGSOR method as an inner iteration for the modified Newton equations to solve the nonlinear system whose Jacobian matrix is a block two-by-two complex symmetric matrix. Our new method is named modified Newton AGSOR (MN-AGSOR) method. Because generalized

We construct smooth finite elements spaces on Powell–Sabin triangulations that form an exact sequence. The first space of the sequence coincides with the classical \(C^1\) Powell–Sabin space, while the others form stable and divergence-free yielding pairs for the Stokes problem. We develop degrees of freedom for these spaces that induce projections that commute with the differential operators.

This paper concerns the approximation of bivariate functions by using the well-known filtered back projection (FBP) formula from computerized tomography. We prove error estimates and convergence rates for the FBP approximation of target functions from Sobolev spaces \(\mathrm H^\alpha ({\mathbb {R}}^2)\) of fractional order \(\alpha >0\), where we bound the FBP approximation error, which is incurred

When a tensor is partitioned into subtensors, some tensor norms of these subtensors form a tensor called a norm compression tensor. Norm compression inequalities for tensors focus on the relation of the norm of this compressed tensor to the norm of the original tensor. We prove that for the tensor spectral norm, the norm of the compressed tensor is an upper bound of the norm of the original tensor

It is shown that the problem of balancing a nonnegative matrix by positive diagonal matrices can be recast as a nonlinear eigenvalue problem with eigenvector nonlinearity. Based on this equivalent formulation some adaptations of the power method and Arnoldi process are proposed for computing the dominant eigenvector which defines the structure of the diagonal transformations. Numerical results illustrate

We explore the potential of Tensor-Train (TT) decompositions in the context of multi-feature face or object recognition strategies. We devise a new recognition algorithm that can handle three or more way tensors in the TT format, and propose a truncation strategy to limit memory usage. Numerical comparisons with other related methods—including the well established recognition algorithm based on high-order

In this paper we analyze the coupling of the Stokes equations with a transport problem modelled by a scalar nonlinear convection–diffusion problem, where the viscosity of the fluid and the diffusion coefficient depend on the solution to the transport problem and its gradient, respectively. An augmented mixed variational formulation for both the fluid flow and the transport model is proposed. As a consequence

An algorithm is proposed for computing intervals containing the Moore–Penrose inverses. For developing this algorithm, we analyze the Ben-Israel iteration. We particularly emphasize that the algorithm is applicable even for rank deficient matrices. Numerical results show that the algorithm is more successful than previous algorithms in the rank deficient cases.

In this paper we consider some applications of Odd and Even Lidstone-type polynomial sequences. In particular we deal with the Odd and Even Lidstone-type and the Generalized Lidstone interpolatory problems with respect to a linear functional \(L_1\) and, respectively, \(L_2\). Estimations of the remainder for the related interpolation polynomials are given. Numerical examples are provided. Some possible

A distributed optimal control problem with the constraint of a parabolic partial differential equation is considered. Boundary value methods are used to solve the coupled initial/final value problems arising from the first order optimality conditions for this problem. We use a block triangular preconditioning strategy for solving the resulting two-by-two linear system. By making use of a matching strategy

In this article, we study the time dependent convection–diffusion–reaction equation coupled with the Darcy equation. We propose and analyze two numerical schemes based on finite element methods for the discretization in space and the implicit Euler method for the discretization in time. An optimal a priori error estimate is then derived for each numerical scheme. Finally, we present some numerical

This paper is concerned with the efficient numerical treatment of 1D stationary Schrödinger equations in the semi-classical limit when including a turning point of first order. As such it is an extension of the paper [3], where turning points still had to be excluded. For the considered scattering problems we show that the wave function asymptotically blows up at the turning point as the scaled Planck

In this paper we propose a novel way to prescribe weakly the symmetry of stress tensors in weak formulations amenable to the construction of mixed finite element schemes. The approach is first motivated in the context of solid mechanics (using, for illustrative purposes, the linear problem of linear elasticity), and then we apply this technique to reduce the computational cost of augmented fully-mixed

Real matrices with non-negative off-diagonal entries play a crucial role for modelling the positive linear dynamical systems. In the literature, these matrices are referred to as Metzler matrices or negated Z-matrices. Finding the closest stable Metzler matrix to an unstable one (and vice versa) is an important issue with many applications. The stability considered here is in the sense of Hurwitz,

For the numerical solution of the general second-order oscillatory system \(y''+ M y = f(y,y')\), You et al. (Numer Algorithm 66:147–176, 2014) proposed the extended Runge–Kutta–Nyström (ERKN) methods. This paper is devoted to symmetric collocation ERKN methods of Gauss and Lobatto IIIA types by Lagrange interpolation. Linear stability of the new ERKN methods is analyzed. Numerical experiments show

The differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system theory, and model order reduction. The few available straight-forward numerical approaches when applied to large-scale systems come with prohibitively large storage requirements. This shortage motivates us to summarize and explore

In this paper, the recursive approach of the Tau method is developed for numerical solution of Abel–Volterra type integral equations. Due to the singular behavior of solutions of these equations, the existing spectral approaches suffer from low accuracy. To overcome this drawback we use Müntz–Legendre polynomials as basis functions which have remarkable approximation to functions with singular behavior

We study the acoustic Helmholtz equation with impedance boundary conditions formulated in terms of velocity, and analyze the stability and convergence properties of lowest-order Raviart-Thomas finite element discretizations. We focus on the high-wavenumber regime, where such discretizations suffer from the so-called “pollution effect”, and lack stability unless the mesh is sufficiently refined. We

In this work, we propose a virtual element method for discretizing the equations that couple the incompressible steady Stokes flow with the Darcy flow by means of the Beaver–Joseph–Saffman condition on their interface. In addition to avoiding explicit expressions of basis functions, this method can not only improve the computational efficiency of any polynomial degree, but also can treat any polygonal

Abstract In this paper, we discuss the following rank-constrained matrix approximation problem in the Frobenius norm: \(\Vert C-AX\Vert =\min \) subject to \( \text{ rk }\left( {C_1 - A_1 X} \right) = b \), where b is an appropriate chosen nonnegative integer. We solve the problem by applying the classical rank-constrained matrix approximation, the singular value decomposition, the quotient singular