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Application of ConvNeXt with transfer learning and data augmentation for malaria parasite detection in resource-limited settings using microscopic images. [PDF]
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Ultrafast visual perception beyond human capabilities enabled by motion analysis using synaptic transistors. [PDF]
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On the Lanczos method and the method of moments
Journal of Physics G: Nuclear Physics, 1978The authors analyse some aspects of the numerically well-behaved Lanczos method of tri-diagonalising a matrix and the mathematically equivalent but numerically disastrous method of moments. It is shown how the elements of the Lanczos tri-diagonal matrix depend only on certain identifiable contributions to the moments, these contributions being those ...
R R Whitehead, A Watt
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On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
SIAM Journal on Numerical Analysis, 1980Theoretical error bounds are established, improving those given by S. Kaniel. Similar inequalities are found for the eigenvectors by using bounds on the acute angle between the exact eigenvectors a...
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The Lanczos method and signal extrapolation
ICASSP '87. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005A technique for signal extrapolation based on the Lanczos method for tridiagonalizing a matrix is discussed. This technique is compared with two previously studied methods, one based on singular value decomposition (SVD) and the other using the conjugate gradient method.
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On the Generalized Lanczos Trust-Region Method
SIAM Journal on Optimization, 2017Summary: The so-called trust-region subproblem gets its name in the trust-region method in optimization and also plays a vital role in various other applications. Several numerical algorithms have been proposed in the literature for solving small-to-medium size dense problems as well as for large-scale sparse problems.
Lei-Hong Zhang +2 more
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Lanczos-type Methods for Continuation Problems
Numerical Linear Algebra with Applications, 1997The authors introduce Lanczos type methods as fast solvers for continuation problems. The symmetric Lanczos method is modified, moreover, for indefinite linear systems. The presented algorithms are used for calculation of simple bifurcation points on the solution curve.
C.-S. Chien, Z.-L. Weng, C.-L. Shen
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A Hermitian Lanczos Method for Normal Matrices
SIAM Journal on Matrix Analysis and Applications, 2002An algorithm is presented for iteratively solving a linear system \(Nx= b\), with a normal matrix \(N\), with an optional 3-term recurrence by extending the Hermitian Lanczos method to normal matrices. To this end the Toeplitz decomposition of \(N\), defined via \(N= H+iK\) with Hermitian \(H\) and \(K\), is employed. The key is to notice that \(N^{-1}\
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Vector-Orthogonality and Lanczos-Type Methods
Numerical Algorithms, 2002A Lanczos-type method, using formal vector orthogonality, is proposed for solving a linear system. An algorithm is given with a strategy being defined to change the dimension of vector orthogonality by increasing or decreasing the dimension, which allow for leading the algorithm and controlling the numerical problem.
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