相关论文: Explicit formulas for efficient multiplication in …

Many interesting and fundamentally practical optimization problems, ranging from optics, to signal processing, to radar and acoustics, involve constraints on the Fourier transform of a function. It is well-known that the {\em fast Fourier…

Multipliers are widely-used arithmetic operators in digital signal processing and machine learning circuits. Due to their relatively high complexity, they can have high latency and be a significant source of power consumption. One strategy…

Various approaches to the numerical representation of the Incomplete Gamma Function F_m(z) for complex arguments z and small integer indexes m are compared with respect to numerical fitness (accuracy and speed). We consider power series,…

In each of the 10 cases with propagators of unit or zero mass, the finite part of the scalar 3-loop tetrahedral vacuum diagram is reduced to 4-letter words in the 7-letter alphabet of the 1-forms $\Omega:=dz/z$ and $\omega_p:=dz/…

This study proposes the "adaptive flip graph algorithm", which combines adaptive searches with the flip graph algorithm for finding fast and efficient methods for matrix multiplication. The adaptive flip graph algorithm addresses the…

Triangular factorizations are an important tool for solving integral equations and partial differential equations with hierarchical matrices ($\mathcal{H}$-matrices). Experiments show that using an $\mathcal{H}$-matrix LR factorization to…

The algorithm reduces the running time of an algorithm of Frieze from O(n^{1.5)) to O(n^(4/3 + o)). It also introduces the concept of admissible permutations that is used in algorithms for obtaining solutions to the AP and the TSP.

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require…

The complexity of software implementations of MDS erasure codes mainly depends on the efficiency of the finite field operations implementation. In this paper, we propose a method to reduce the complexity of the finite field multiplication…

Recent years have seen renewed attention to arithmetic coding (AC). This is thanks to the use of AC for distribution matching (DM) to control the channel input distribution in probabilistic amplitude shaping. There are two main problems…

The Fast Multipole Method (FMM) reduces the computation of pairwise two-body interactions among $N$-particles to order $N$, whose computation cost should be of order $N^2$ by brute force. However, its implementation is somewhat complicated…

We consider the famous Strassen algorithm for fast multiplication of matrices. We show that this algorithm has a nontrivial finite group of automorphisms of order 36 (namely the direct product of two copies of the symmetric group on 3…

Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…

Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…

Cryptographic schemes like Fully Homomorphic Encryption (FHE) and Zero-Knowledge Proofs (ZKPs), while offering powerful privacy-preserving capabilities, are often hindered by their computational complexity. Polynomial multiplication, a core…

The flip graph algorithm is a method for discovering new matrix multiplication schemes by following random walks on a graph. We introduce a version of the flip graph algorithm for matrix multiplication schemes that admit certain symmetries.…

In this paper, we present an advanced analysis of near optimal algorithms that use limited space to solve the frequency estimation, heavy hitters, frequent items, and top-k approximation in the bounded deletion model. We define the family…

In this paper, we propose a new stochastic alternating direction method of multipliers (ADMM) algorithm, which incrementally approximates the full gradient in the linearized ADMM formulation. Besides having a low per-iteration complexity as…

Hashing has been widely used for efficient similarity search based on its query and storage efficiency. To obtain better precision, most studies focus on designing different objective functions with different constraints or penalty terms…

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to…