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Structured canonical forms under unitary and suitable structure-preserving similarity transformations for normal and (skew-)Hamiltonian as well as normal and per(skew)-Hermitian matrices are proposed. Moreover, an algorithm for computing…
Bayesian Optimization (BO) has shown great promise for the global optimization of functions that are expensive to evaluate, but despite many successes, standard approaches can struggle in high dimensions. To improve the performance of BO,…
In this paper, we propose, analyze and demonstrate a dynamic momentum method to accelerate power and inverse power iterations with minimal computational overhead. The method can be applied to real diagonalizable matrices, is provably…
A family of symmetric matrices $A_1,\ldots, A_d$ is SDC (simultaneous diagonalization by congruence, also called non-orthogonal joint diagonalization) if there is an invertible matrix $X$ such that every $X^T A_k X$ is diagonal. In this…
Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…
This paper proposes and analyzes Riemannian optimization algorithms on the manifold of unitary and symmetric matrices, denoted ${\cal {U}}_s$, which naturally models the scattering matrices of passive and reciprocal devices such as…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…
In this work we give an efficient construction of unitary $k$-designs using $\tilde{O}(k\cdot poly(n))$ quantum gates, as well as an efficient construction of a parallel-secure pseudorandom unitary (PRU). Both results are obtained by giving…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…
The power method is a basic method for computing the dominant eigenpair of a matrix. In this paper, we propose a structure-preserving power-like method for computing the dominant conjugate pair of purely imaginary eigenvalues and the…
Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…
A counterpart of the modular double for quantum superalgebra $\cU_q(\osp(1|2))$ is constructed by means of supersymmetric quantum mechanics. We also construct the $R$-matrix operator acting in the corresponding representations, which is…
We consider the problem of minimizing a non-convex function over a smooth manifold $\mathcal{M}$. We propose a novel algorithm, the Orthogonal Directions Constrained Gradient Method (ODCGM) which only requires computing a projection onto a…
Some skew-symmetrizable integer exchange matrices are associated to ideal (tagged) triangulations of marked bordered surfaces. These exchange matrices admits unfoldings to skew-symmetric matrices. We develop an combinatorial algorithm that…
In this paper, an algorithm for construction of multiple sets of two dimensional (2D) or matrix unipolar (optical) orthogonal codes has been proposed. Representations of these 2D codes in difference of positions representation (DoPR) have…
Structure learning methods for covariance and concentration graphs are often validated on synthetic models, usually obtained by randomly generating: (i) an undirected graph, and (ii) a compatible symmetric positive definite (SPD) matrix. In…
Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…
We present a fast direct algorithm for computing symmetric factorizations, i.e. $A = WW^T$, of symmetric positive-definite hierarchical matrices with weak-admissibility conditions. The computational cost for the symmetric factorization…
Many numerical methods for evaluating matrix functions can be naturally viewed as computational graphs. Rephrasing these methods as directed acyclic graphs (DAGs) is a particularly effective approach to study existing techniques, improve…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…