Related papers: Faster Walsh-Hadamard Transform and Matrix Multipl…
We give algorithms with lower arithmetic operation counts for both the Walsh-Hadamard Transform (WHT) and the Discrete Fourier Transform (DFT) on inputs of power-of-2 size $N$. For the WHT, our new algorithm has an operation count of…
For every fixed constant $\alpha > 0$, we design an algorithm for computing the $k$-sparse Walsh-Hadamard transform of an $N$-dimensional vector $x \in \mathbb{R}^N$ in time $k^{1+\alpha} (\log N)^{O(1)}$. Specifically, the algorithm is…
Recovering a signal (function) from finitely many binary or Fourier samples is one of the core problems in modern medical imaging, and by now there exist a plethora of methods for recovering a signal from such samples. Examples of methods,…
A hybrid classical-quantum approach for evaluation of multi-dimensional Walsh-Hadamard transforms and its applications to quantum image processing are proposed. In this approach, multidimensional Walsh-Hadamard transforms are obtained using…
A new iterative low complexity algorithm has been presented for computing the Walsh-Hadamard transform (WHT) of an $N$ dimensional signal with a $K$-sparse WHT, where $N$ is a power of two and $K = O(N^\alpha)$, scales sub-linearly in $N$…
Nowadays computational complexity of fast walsh hadamard transform and nonlinearity for Boolean functions and large substitution boxes is a major challenge of modern cryptography research on strengthening encryption schemes against linear…
A hybrid classical-quantum approach for the solution of nonlinear ordinary differential equations using Walsh-Hadamard basis functions is proposed. Central to this hybrid approach is the computation of the Walsh-Hadamard transform of…
We develop several efficient algorithms for the classical \emph{Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input $n\times n$ matrix $A$, this…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
For a matrix $M$ and a positive integer $r$, the rank $r$ rigidity of $M$ is the smallest number of entries of $M$ which one must change to make its rank at most $r$. There are many known applications of rigidity lower bounds to a variety…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
The decomposition of a square matrix into a sum of Pauli strings is a classical pre-processing step required to realize many quantum algorithms. Such a decomposition requires significant computational resources for large matrices. We…
We provide fast algorithms for overconstrained $\ell_p$ regression and related problems: for an $n\times d$ input matrix $A$ and vector $b\in\mathbb{R}^n$, in $O(nd\log n)$ time we reduce the problem $\min_{x\in\mathbb{R}^d} \|Ax-b\|_p$ to…
Johnson-Lindenstrauss embeddings are widely used to reduce the dimension and thus the processing time of data. To reduce the total complexity, also fast algorithms for applying these embeddings are necessary. To date, such fast algorithms…
A recently discovered universal rank-based matrix method to extract trends from noisy time series is described in [1] but the formula for the output matrix elements, implemented there as an open-access supplement MATLAB computer code, is…
We consider the problem of computing the Walsh-Hadamard Transform (WHT) of some $N$-length input vector in the presence of noise, where the $N$-point Walsh spectrum is $K$-sparse with $K = {O}(N^{\delta})$ scaling sub-linearly in the input…
Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
The Hadamard decomposition is a powerful technique for data analysis and matrix compression, which decomposes a given matrix into the element-wise product of two or more low-rank matrices. In this paper, we develop an efficient algorithm to…
Many standard conversion matrices between coefficients in classical orthogonal polynomial expansions can be decomposed using diagonally-scaled Hadamard products involving Toeplitz and Hankel matrices. This allows us to derive…