Practical improvement of the divide-and-conquer eigenvalue algorithms

DOI10.1007/BF02241709zbMath0756.65053OpenAlexW135489932MaRDI QIDQ1192014

Dario Andrea Bini, Pan, Victor Y.

Publication date: 27 September 1992

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02241709

zbMATH Keywords

clusteringeigenvaluesnumerical experimentsnumerical stabilityeffectivenesssymmetric tridiagonal matrixcomputational costdivide-and-conquer algorithms

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Complexity and performance of numerical algorithms (65Y20)

Related Items

Computations with quasiseparable polynomials and matrices, Unnamed Item, Nearly optimal refinement of real roots of a univariate polynomial, Computation of Darboux polynomials and rational first integrals with bounded degree in polynomial time, Improving the solution of the symmetric eigenvalue problem and an extension, Efficient parallel factorization and solution of structured and unstructured linear systems

Cites Work

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• Eigenvalues of a symmetric tridiagonal matrix: A divide-and-conquer approach
• On the worst-case arithmetic complexity of approximating zeros of polynomials
• A Divide and Conquer method for the symmetric tridiagonal eigenproblem
• Rank-one modification of the symmetric eigenproblem
• Iteration schemes for the divide-and-conquer eigenvalue solver
• An $O(N^2 )$ Method for Computing the Eigensystem of $N \times N$ Symmetric Tridiagonal Matrices by the Divide and Conquer Approach
• A Fully Parallel Algorithm for the Symmetric Eigenvalue Problem
• Eigenvalues of Symmetric Tridiagonal Matrices: A Fast, Accurate and Reliable Algorithm