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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 symmetric matrices, can compute the eigenvector/eigenvalue pair to essentially arbitrary precision, and with minor modifications can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications.
Quantum walks are widely and successfully used to model diverse physical processes. This leads to computation of the models, to explore their properties. Quantum walks have also been shown to be universal for quantum computing. This is a more subtle
We describe an explicit algorithm to factorize an even antisymmetric N^2 matrix into triangular and trivial factors. This allows for a straight forward computation of Pfaffians (including their signs) at the cost of N^3/3 flops.
We investigate eigenvectors of rank-one deformations of random matrices $boldsymbol B = boldsymbol A + theta boldsymbol {uu}^*$ in which $boldsymbol A in mathbb R^{N times N}$ is a Wigner real symmetric random matrix, $theta in mathbb R^+$, and $bold
We prove localization with high probability on sets of size of order $N/log N$ for the eigenvectors of non-Hermitian finitely banded $Ntimes N$ Toeplitz matrices $P_N$ subject to small random perturbations, in a very general setting. As perturbation
We propose a new algorithm to compute the X-ray transform of an image represented by unit (pixel/voxel) basis functions. The fundamental issue is equivalently calculating the intersection lengths of the ray with associated units. For any given ray, w