Related papers: A stable semi-implicit algorithm
We consider a nonlinear autonomous system of $N\gg 1$ degrees of freedom randomly coupled by both relaxational ('gradient') and non-relaxational ('solenoidal') random interactions. We show that with increased interaction strength such…
As a common generalization of previously solved optimization problems concerning bipartite stable matchings, we describe a strongly polynomial network flow based algorithm for computing $\ell$ disjoint stable matchings with minimum total…
Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Explicit Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems…
For discrete spectrum of 1D second-order differential/difference operators (with or without potential (killing), with the maximal/minimal domain), a pair of unified dual criteria are presented in terms of two explicit measures and the…
By means of a linear scaling of the variables we convert a singular bifurcation equation in $\R^n$ into an equivalent equation to which the classical implicit function theorem can be directly applied. This allows to deduce the existence of…
When learning stable linear dynamical systems from data, three important properties are desirable: i) predictive accuracy, ii) verifiable stability, and iii) computational efficiency. Unconstrained minimization of prediction errors leads to…
In the numerical solution of partial differential equations using a method-of-lines approach, the availability of high order spatial discretization schemes motivates the development of sophisticated high order time integration methods. For…
We study and derive algorithms for nonlinear eigenvalue problems, where the system matrix depends on the eigenvector, or several eigenvectors (or their corresponding invariant subspace). The algorithms are derived from an implicit…
The phase field method is an effective tool for modeling microstructure evolution in materials. Many efficient implicit numerical solvers have been proposed for phase field simulations under uniform and time-invariant model parameters. We…
Time integration methods for solving initial value problems are an important component of many scientific and engineering simulations. Implicit time integrators are desirable for their stability properties, significantly relaxing…
Maxwell's equations are considered with transparent boundary conditions, for initial conditions and inhomogeneity having support in a bounded, not necessarily convex three-dimensional domain or in a collection of such domains. The numerical…
In this work, we consider the development of implicit explicit total variation diminishing (TVD) methods (also termed SSP: strong stability preserving) for the compressible isentropic Euler system in the low Mach number regime. The scheme…
In this paper, we consider the problem of stabilizing discrete-time linear systems by computing a nearby stable matrix to an unstable one. To do so, we provide a new characterization for the set of stable matrices. We show that a matrix $A$…
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems. Their convergence rates have been established by a growing body of…
Dynamical systems with sub-processes evolving on many different time scales are ubiquitous in applications. Their efficient solution is greatly enhanced by automatic time step variation. This paper is concerned with the theory, construction…
In this work, we develop analysis and algorithms for a class of (stochastic) bilevel optimization problems whose lower-level (LL) problem is strongly convex and linearly constrained. Most existing approaches for solving such problems rely…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…