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The Algebraic Eigenvalue Problem
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This article is published in Mathematics of Computation.The article was published on 1966-10-01. It has received 2408 citations till now. The article focuses on the topics: Algebraic number & Eigenvalues and eigenvectors.read more
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Deep learning in neural networks
TL;DR: This historical survey compactly summarizes relevant work, much of it from the previous millennium, review deep supervised learning, unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.
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LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
TL;DR: Numerical tests are described comparing I~QR with several other conjugate-gradient algorithms, indicating that I ~QR is the most reliable algorithm when A is ill-conditioned.
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The Geometry of Algorithms with Orthogonality Constraints
TL;DR: The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms and developers of new algorithms and perturbation theories will benefit from the theory.
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Direct least squares fitting of ellipses
TL;DR: This paper presents a new efficient method for fitting ellipses to scattered data that is ellipse-specific so that even bad data will always return an ellipso, and can be solved naturally by a generalized eigensystem.
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Nineteen Dubious Ways to Compute the Exponential of a Matrix
Cleve B. Moler,Charles Van Loan +1 more
TL;DR: In this article, the exponential of a matrix could be computed in many ways, including approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial.