Related papers: Fast algorithm of adaptive Fourier series
The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
We study greedy-type algorithms such that at a greedy step we pick several dictionary elements contrary to a single dictionary element in standard greedy-type algorithms. We call such greedy algorithms {\it super greedy algorithms}. The…
A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…
We study the fundamental problem of selecting optimal features for model construction. This problem is computationally challenging on large datasets, even with the use of greedy algorithm variants. To address this challenge, we extend the…
The selection problem of an optimal set of sensors estimating the snapshot of high-dimensional data is considered. The objective functions based on various criteria of optimal design are adopted to the greedy method: D-optimality,…
We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not…
We present Scaff-PD, a fast and communication-efficient algorithm for distributionally robust federated learning. Our approach improves fairness by optimizing a family of distributionally robust objectives tailored to heterogeneous clients.…
This article develops a new theoretical basis for decomposing signals that are formed by the linear superposition of a finite number of modes. Each mode depends nonlinearly upon several parameters; we seek both these parameters and the…
This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards)…
The proliferation of the Internet of Things (IoT) and widespread use of devices with sensing, computing, and communication capabilities have motivated intelligent applications empowered by artificial intelligence. The classical artificial…
Preferential attachment lies at the heart of many network models aiming to replicate features of real world networks. To simulate the attachment process, conduct statistical tests, or obtain input data for benchmarks, efficient algorithms…
In this work, we propose an algorithm for a filter based on the Fast Fourier Transform (FFT), which, due to its characteristics, allows for an efficient computational implementation, ease of use, and minimizes amplitude variation in the…
The determinantal point process (DPP) is an elegant probabilistic model of repulsion with applications in various machine learning tasks including summarization and search. However, the maximum a posteriori (MAP) inference for DPP which…
In this letter, a fast Fourier transform (FFT)-enhanced low-complexity super-resolution sensing algorithm for near-field source localization with both angle and range estimation is proposed. Most traditional near-field source localization…
Automatic differentiation (AD) is a technique for computing the derivative of a function represented by a program. This technique is considered as the de-facto standard for computing the differentiation in many machine learning and…
In the field of digital signal processing, the fast Fourier transform (FFT) is a fundamental algorithm, with its processors being implemented using either the pipelined architecture, well-known for high-throughput applications but weak in…
Paraxial diffraction modeling based on the Fourier transform has seen widespread implementation for simulating the response of a diffraction-limited optical system. For systems where the paraxial assumption is not sufficient, a class of…
In this paper, we propose a new paradigm for program optimization which is based on aggressive aggregation, i.e., on a partial evaluation-based decomposition of acyclic program fragments into a pair of computationally optimal structures: an…
For smooth finite fields $F_q$ (i.e., when $q-1$ factors into small primes) the Fast Fourier Transform (FFT) leads to the fastest known algebraic algorithms for many basic polynomial operations, such as multiplication, division,…