Related papers: A faster hafnian formula for complex matrices and …
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
We present two fast algorithms for matrix-vector multiplication $y=Ax$, where $A$ is a Hankel matrix. The current asymptotically fastest method is based on the Fast Fourier Transform (FFT), however in multiprecision arithmetics with very…
We consider the quantum complexity of estimating matrix elements of unitary irreducible representations of groups. For several finite groups including the symmetric group, quantum Fourier transforms yield efficient solutions to this…
In this paper, we study quantum algorithms of matrix multiplication from the viewpoint of inputting quantum/classical data to outputting quantum/classical data. The main target is trying to overcome the input and output problem, which are…
We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since…
We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the…
We present two conjectures regarding the running time of computing symmetric factorizations for a Hankel matrix $\mathbf{H}$ and its inverse $\mathbf{H}^{-1}$ as $\mathbf{B}\mathbf{B}^*$ under fixed-point arithmetic. If solved, these would…
We analyze the parallel performance of randomized interpolative decomposition by decomposing low rank complex-valued Gaussian random matrices up to 64 GB. We chose a Cray XMT supercomputer as it provides an almost ideal PRAM model…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
We propose a fast algorithm for computing the economic capital, Value at Risk and Greeks in the Gaussian factor model. The algorithm proposed here is much faster than brute force Monte Carlo simulations or Fourier transform based methods…
A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…
We calculate convergent 3-loop Feynman diagrams containing a single massive loop equipped with twist $\tau =2$ local operator insertions corresponding to spin $N$. They contribute to the massive operator matrix elements in QCD describing…
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time. Essential for the PFD computation is the construction of the…
There are many representations of planar graphs, but few are as elegant as Tur\'an's (1984): it is simple and practical, uses only 4 bits per edge, can handle self-loops and multi-edges, and can store any specified embedding. Its main…
We revisit the fundamental Boolean Matrix Multiplication (BMM) problem. With the invention of algebraic fast matrix multiplication over 50 years ago, it also became known that BMM can be solved in truly subcubic $O(n^\omega)$ time, where…
We estimate the Boolean complexity of multiplication of structured matrices by a vector and the solution of nonsingular linear systems of equations with these matrices. We study four basic most popular classes, that is, Toeplitz, Hankel,…