Rescaling matrix: if the operation is k times equation i, put the number k at the position (row=i, col=i) of an identity matrix. Row 1 multiply by constant 3. (Image by Author) Pivoting matrix: if a multiple of equation i is added to equation j, put the number k at the position...
This paper presents a hybrid variational quantum algorithm that finds a random eigenvector of a unitary matrix with a known quantum circuit. The algorithm
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then the SVD providesmatrices U, S, and V'. IIRC, the eigenvalues of D'D (the covariancematrix of interest) are then packed along the first dimension of V',and the eigenvalues are the square of the values in S.
Rust Chebyshev Proxy Rootfinder: A robust global rootfinder using adaptive Chebyshev interpolation with automatic subdivision that accurately finds all roots of a smooth function F(x) on [a, b] using the Chebyshev-Frobenius companion matrix. polynomial rootfinding chebyshev-polynomial chebyshev-interpolat...
The dynamic mode decomposition (DMD) is an equation-free, data-driven matrix decomposition that is capable of providing accurate reconstructions of spatio-temporal coherent structures arising in nonlinear dynamical systems, or short-time future estimates of such systems. The DMD method provides a regres...