Related papers: Craig Interpolation and Access Interpolation with …
In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of…
Let $G$ be a commutative algebraic group embedded in projective space and $\Gamma$ a finitely generated subgroup of $G$. From these data we construct a chain of algebraic subgroups of $G$ which is intimately related to obstructions to…
We consider quadrature formulas based on interpolation using the basis functions $1/(1+t_kx)$ $(k=1,2,3,\ldots)$ on $[-1,1]$, where $t_k$ are parameters on the interval $(-1,1)$. We investigate two types of quadratures: quadrature formulas…
Priest has provided a simple tableau calculus for Chellas's conditional logic Ck. We provide rules which, when added to Priest's system, result in tableau calculi for Chellas's CK and Lewis's VC. Completeness of these tableaux, however,…
Primal-dual algorithms are frequently used for iteratively solving large-scale convex optimization problems. The analysis of such algorithms is usually done on a case-by-case basis, and the resulting guaranteed rates of convergence can be…
The relational semantics of linear logic is a powerful framework for defining resource-aware models of the $\lambda$-calculus. However, its quantitative aspects are not reflected in the preorders and equational theories induced by these…
In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order cell-centered finite-volume discretization on tetrahedral…
The worst-case performance of an optimization method on a problem class can be analyzed using a finite description of the problem class, known as interpolation conditions. In this work, we study interpolation conditions for linear operators…
Proof schemata are a variant of LK-proofs able to simulate various induction schemes in first-order logic by adding so called proof links to the standard first-order LK-calculus. Proof links allow proofs to reference proofs thus giving…
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
Vector extrapolation methods are widely used in large-scale simulation studies, and numerous extrapolation-based acceleration techniques have been developed to enhance the convergence of linear and nonlinear fixed-point iterative methods.…
We consider rank-one non-symmetric tensor estimation and derive simple formulas for the mutual information. We start by the order 2 problem, namely matrix factorization. We treat it completely in a simpler fashion than previous proofs using…
Abstraction is a successful technique in software verification, and interpolation on infeasible error paths is a successful approach to automatically detect the right level of abstraction in counterexample-guided abstraction refinement.…
We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…
The versatility of data-driven approximation by interpolatory methods, originally settled for model approximation purpose, is illustrated in the context of linear controller design and stability analysis of irrational models. To this aim,…
Coupled-cluster theory is a powerful tool for first-principles calculations of atomic nuclei, enabling accurate predictions of nuclear observables across the Segr\`e chart. While coupled-cluster computations are especially efficient at…
The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of…
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
The Floater--Hormann family of rational interpolants do not have spurious poles or unattainable points, are efficient to calculate, and have arbitrarily high approximation orders. One concern when using them is that the amplification of…
When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…