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In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…
We give faster algorithms and improved sample complexities for estimating the top eigenvector of a matrix $\Sigma$ -- i.e. computing a unit vector $x$ such that $x^T \Sigma x \ge (1-\epsilon)\lambda_1(\Sigma)$: Offline Eigenvector…
The iterative algorithm recently proposed by Waxman for solving eigenvalue problems, which relies on the method of moments, has been modified to improve its convergence considerably without sacrificing its benefits or elegance. The…
This paper adapts look-ahead and backward finite difference formulas to compute future eigenvectors and eigenvalues of piecewise smooth time-varying symmetric matrix flows $A(t)$. It is based on the Zhang Neural Network (ZNN) model for…
Model quantization enables the deployment of deep neural networks under resource-constrained devices. Vector quantization aims at reducing the model size by indexing model weights with full-precision embeddings, i.e., codewords, while the…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
Eigenvalue analysis is widely used for linear instability analysis in both external and internal aerodynamics. It typically involves finding the steady state, linearizing around it to obtain the Jacobian, and then solving for its…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the…
We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…
We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix by solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of…
We present a new approach to compute selected eigenvalues and eigenvectors of the two-parameter eigenvalue problem. Our method requires computing generalized eigenvalue problems of the same size as the matrices of the initial two-parameter…
We introduce a new Projected Rayleigh Quotient Iteration aimed at improving the convergence behaviour of classic Rayleigh Quotient iteration (RQI) by incorporating approximate information about the target eigenvector at each step. While…
We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters,…
The standard approach for finding eigenvalues and eigenvectors of matrix polynomials starts by embedding the coefficients of the polynomial into a matrix pencil, known as linearization. Building on the pioneering work of Nakatsukasa and…
Convergence analysis of block iterative solvers for Hermitian eigenvalue problems and the closely related research on properties of matrix-based signal filters are challenging, and attract increasing attention due to their recent…
We consider the reflection equation algebra for a finite dimensional R-matrix for the $(h,w)$-deformed Heisenberg algebra ${\cal U}_{h,w}(h(4))$. A representation of the reflection matrix $K$ is constructed using the matrix generators…
The classic method for computing the spectral decomposition of a real symmetric matrix, the Jacobi algorithm, can be accelerated by using mixed precision arithmetic. The Jacobi algorithm is aiming to reduce the off-diagonal entries…
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…
We develop explicit formulae for the eigenvalues of various invariants for highest weight irreducible representations of the quantum supergroup $U_q[gl(m|n)]$. The techniques employed make use of modified characteristic identity methods and…