Related papers: Solving the 3x3 Real Symmetric Eigenproblem
Quartic eigenvalue problem $(\lambda^4 A + \lambda^3 B + \lambda^2C + \lambda D + E)x = \mathbf{0}$ naturally arises e.g. when solving the Orr-Sommerfeld equation in the analysis of the stability of the {Poiseuille} flow, in theoretical…
The previously reported neBEM solver has been used to solve electrostatic problems having three-dimensional edges and corners in the physical domain. Both rectangular and triangular elements have been used to discretize the geometries under…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
The paper presents investigations on the implementation and performance of the finite element numerical integration algorithm for first order approximations and three processor architectures, popular in scientific computing, classical CPU,…
A graph is said to be rigid if, given a generic realisation of the graph as a bar-and-joint framework in the plane, there exist only finitely many other realisations of the graph with the same edge lengths modulo rotations, reflections and…
The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…
This paper introduces bootstrap multigrid methods for solving eigenvalue problems arising from the discretization of partial differential equations. Inspired by the full bootstrap algebraic multigrid (BAMG) setup algorithm that includes an…
We consider linear parameter-dependent systems $A(\mu) x(\mu) = b$ for many different $\mu$, where $A$ is large and sparse, and depends nonlinearly on $\mu$. Solving such systems individually for each $\mu$ would require great computational…
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible…
We show that the following algorithmic problem is decidable: given a $2$-dimensional simplicial complex, can it be embedded (topologically, or equivalently, piecewise linearly) in $\mathbf{R}^3$? By a known reduction, it suffices to decide…
In this paper, we describe a new hybrid algorithm for computing all singular triplets above a given threshold and provide its implementation in MATLAB/Octave and R. The high performance of our codes and ease at which they can be used,…
We present efficient algorithms for detecting central and mirror symmetry for the case of algebraic curves defined by means of polynomial parametrizations. The algorithms are based on the existence of a linear relationship between two…
We consider fourth order singularly perturbed eigenvalue problems in one-dimension and the approximation of their solution by the $h$ version of the Finite Element Method (FEM). In particular, we use piecewise Hermite polynomials of degree…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. This framework includes well known graph problems such as Minimum…
The history of research on eigenvalue problems is rich with many outstanding contributions. Nonetheless, the rapidly increasing size of data sets requires new algorithms for old problems in the context of extremely large matrix dimensions.…
Given a set of $n$ distinct real numbers, our goal is to form a symmetric, unreduced, tridiagonal, matrix with those numbers as eigenvalues. We give an algorithm which is a stable implementation of a naive algorithm forming the…
In graph modification problems, one is given a graph G and the goal is to apply a minimum number of modification operations (such as edge deletions) to G such that the resulting graph fulfills a certain property. For example, the Cluster…