Springer Science and Business Media LLC
Công bố khoa học tiêu biểu
* Dữ liệu chỉ mang tính chất tham khảo
Sắp xếp:
Zigzag Persistence
Springer Science and Business Media LLC - Tập 10 - Trang 367-405 - 2010
We describe a new methodology for studying persistence of topological features across a family of spaces or point-cloud data sets, called zigzag persistence. Building on classical results about quiver representations, zigzag persistence generalises the highly successful theory of persistent homology and addresses several situations which are not covered by that theory. In this paper we develop the...... hiện toàn bộ
A New Approach to the Analysis of Parametric Finite Element Approximations to Mean Curvature Flow
Springer Science and Business Media LLC - - Trang 1-65 - 2023
Parametric finite element methods have achieved great success in approximating the evolution of surfaces under various different geometric flows, including mean curvature flow, Willmore flow, surface diffusion, and so on. However, the convergence of Dziuk’s parametric finite element method, as well as many other widely used parametric finite element methods for these geometric flows, remains open....... hiện toàn bộ
Whitney Estimates for Convex Domains with Applications to Multivariate Piecewise Polynomial Approximation
Springer Science and Business Media LLC - Tập 4 - Trang 345-368 - 2004
We prove the following Whitney estimate. Given 0 < p \le \infty,
r \in N, and d \ge 1, there exists a constant C(d,r,p),
depending only on the three parameters, such that for every
bounded convex domain Ω \subset Rd, and each function
f \in Lp(Ω),
Er-1(f,Ω)p \le C(d,r,p)ωr(f, diam(Ω))p,
where Er-1(f,Ω)p is the degree of
approximation by polynomials of total degree, r – 1, and
ωr(f,·)p is the ...... hiện toàn bộ
A Geometric Framework for Stochastic Shape Analysis
Springer Science and Business Media LLC - Tập 19 Số 3 - Trang 653-701 - 2019
Discrete Lie Advection of Differential Forms
Springer Science and Business Media LLC - Tập 11 - Trang 131-149 - 2010
In this paper, we present a numerical technique for performing Lie advection of arbitrary differential forms. Leveraging advances in high-resolution finite-volume methods for scalar hyperbolic conservation laws, we first discretize the interior product (also called contraction) through integrals over Eulerian approximations of extrusions. This, along with Cartan’s homotopy formula and a discrete e...... hiện toàn bộ
An Accelerated First-Order Method for Non-convex Optimization on Manifolds
Springer Science and Business Media LLC - Tập 23 - Trang 1433-1509 - 2022
We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical points faster than regular gradient descent. A randomized version also finds approximate second-order critical points. Both the algorithms and ...... hiện toàn bộ
Computability in Harmonic Analysis
Springer Science and Business Media LLC - Tập 22 - Trang 849-873 - 2021
We study the question of constructive approximation of the harmonic measure
$$\omega _x^\varOmega $$
of a bounded domain
$$\varOmega $$
with respect to a point
...... hiện toàn bộ
Superinterpolation in Highly Oscillatory Quadrature
Springer Science and Business Media LLC - Tập 12 - Trang 203-228 - 2011
Asymptotic expansions for oscillatory integrals typically depend on the values and derivatives of the integrand at a small number of critical points. We show that using values of the integrand at certain complex points close to the critical points can actually yield a higher asymptotic order approximation to the integral. This superinterpolation property has interesting ramifications for numerical...... hiện toàn bộ
Complexity of Bezout’s Theorem VI: Geodesics in the Condition (Number) Metric
Springer Science and Business Media LLC - Tập 9 - Trang 171-178 - 2007
We introduce a new complexity measure of a path of (problems, solutions) pairs in terms of the length of the path in the condition metric which we define in the article. The measure gives an upper bound for the number of Newton steps sufficient to approximate the path discretely starting from one end and thus produce an approximate zero for the endpoint. This motivates the study of short paths or...... hiện toàn bộ
Generating the Greatest Common Divisor, and Limitations of Primitive Recursive Algorithms
Springer Science and Business Media LLC - Tập 3 - Trang 297-324 - 2002
The greatest common divisor of two integers cannot be
generated in a uniformly bounded number of steps from those integers
using arithmetic operations. The proof uses an elementary model-theoretic
construction that enables us to focus on
“integers with transcendental ratio.”
This unboundedness result is part of the solution of a problem posed
by Y. Moschovakis on limitations of primitive recu...... hiện toàn bộ
Tổng số: 515
- 1
- 2
- 3
- 4
- 5
- 6
- 10