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Multigrid is one of the most efficient methods for solving large-scale linear systems that arise from discretized partial differential equations. As a foundation for multigrid analysis, two-grid theory plays an important role in motivating…
We consider a fast, data-sparse directional method to realize matrix-vector products related to point evaluations of the Helmholtz kernel. The method is based on a hierarchical partitioning of the point sets and the matrix. The considered…
This article is concerned with a new filtered two-step variational integrator for solving the charged-particle dynamics in a mildly non-uniform moderate or strong magnetic field with a dimensionless parameter $\varepsilon$ inversely…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
We present a major revamp of the point-location data structure for general two-dimensional subdivisions via randomized incremental construction, implemented in CGAL, the Computational Geometry Algorithms Library. We can now guarantee that…
We present an efficient multi-accuracy algorithm for the computations of a set of special functions of a complex argument, z=x+iy. These functions include the complex probability function w(z), and closely related functions such as the…
The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…
To achieve high data rates defined in 5G, the use of millimeter-waves and massive-MIMO are indispensable. To benefit from these technologies, an accurate estimation of the channel parameters is crucial. We propose a novel two-stage…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…
Directional interpolation is a fast and efficient compression technique for high-frequency Helmholtz boundary integral equations, but it requires a very large amount of storage in its original form. Algebraic recompression can significantly…
We construct an algorithm for implementing the discrete wavelet transform by means of matrices in SO_2(R) for orthonormal compactly supported wavelets and matrices in SL_m(R), m > = 2, for compactly supported biorthogonal wavelets. We show…
Video frame interpolation is an important low-level vision task, which can increase frame rate for more fluent visual experience. Existing methods have achieved great success by employing advanced motion models and synthesis networks.…
Variational Bayes (VB) has become a widely-used tool for Bayesian inference in statistics and machine learning. Nonetheless, the development of the existing VB algorithms is so far generally restricted to the case where the variational…
We propose a numerical interferometry method for identification of optical multiply-scattering systems when only intensity can be measured. Our method simplifies the calibration of optical transmission matrices from a quadratic to a linear…
We describe an efficient implementation of a hierarchy of algorithms for multiplication of dense matrices over the field with two elements (GF(2)). In particular we present our implementation -- in the M4RI library -- of Strassen-Winograd…
We present a new mixed-integer programming (MIP) approach for offline multiple change-point detection by casting the problem as a globally optimal piecewise linear (PWL) fitting problem. Our main contribution is a family of strengthened MIP…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…