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In order to accelerate the subset computation of eigenpairs for real symmetric tridiagonal matrices on shared-memory multi-core processors, a parallel symmetric tridiagonal eigensolver is proposed, which computes eigenvalues of target matrices using the parallel bisection algorithm and computes the corresponding eigenvectors using the block inverse iteration algorithm with reorthogonalization (BIR...
Effective GPU implementations of an inverse iteration algorithm with reorthogonalization are proposed for computing eigenvectors of symmetric tridiagonal matrices. The key to effectively accelerating the inverse iteration algorithm in GPU computing is the adoption of reorthogonalization code optimal for the GPU. The CGS2 algorithm and the compact WY orthogonalization algorithm, which can be implemented...
The discrete Lotka-Volterra algorithm for computing matrix singular values is considered. Positivity and boundedness of a parameter and variables are shown to guarantee a numerical stability of the algorithm. Orthogonal polynomials and integrable systems play a key role
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