相关论文: Approximation algorithms for wavelet transform cod…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which…
This paper is concerned with near-optimal approximation of a given function $f \in L_2([0,1])$ with elements of a polynomially enriched wavelet frame, a so-called quarklet frame. Inspired by $hp$-approximation techniques of Binev, we use…
In this paper, we develop a wavelet-based theoretical framework for analyzing the universal approximation capabilities of neural networks over a wide range of activation functions. Leveraging wavelet frame theory on the spaces of…
Most commonly used \emph{adaptive} algorithms for univariate real-valued function approximation and global minimization lack theoretical guarantees. Our new locally adaptive algorithms are guaranteed to provide answers that satisfy a…
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…
Work on approximate linear algebra has led to efficient distributed and streaming algorithms for problems such as approximate matrix multiplication, low rank approximation, and regression, primarily for the Euclidean norm $\ell_2$. We study…
We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The Hankel-norm approximation is a model reduction method which provides the best approximation in the Hankel semi-norm. In this paper the computation of the optimal Hankel-norm approximation is generalized to the case of linear…
While the problem of approximate nearest neighbor search has been well-studied for Euclidean space and $\ell_1$, few non-trivial algorithms are known for $\ell_p$ when ($2 < p < \infty$). In this paper, we revisit this fundamental problem…
Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…
Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
Function approximation using Haar basis systems offers an efficient implementation when compressed via Patricia trees while retaining the flexibility of wavelets for both global and local fitting. However, like B-spline-based…