The LAPW Method with Eigendecomposition Based on the Hari--Zimmermann Generalized Hyperbolic SVD

DOI10.1137/19M1277813zbMath1452.65071arXiv1907.08560OpenAlexW3088632199MaRDI QIDQ5131986

Edoardo Di Napoli, Vedran Novaković, Gayatri Čaklović, Sanja Singer

Publication date: 9 November 2020

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.08560

zbMATH Keywords

generalized singular value decompositionhyperbolic QR factorizationgeneralized eigendecomposition

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Parallel numerical computation (65Y05) Applications to the sciences (65Z05) Orthogonalization in numerical linear algebra (65F25)

Related Items (6)

A Kogbetliantz-type algorithm for the hyperbolic SVD ⋮ Batched Computation of the Singular Value Decompositions of Order Two by the AVX-512 Vectorization ⋮ Vectorization of a Thread-Parallel Jacobi Singular Value Decomposition Method ⋮ On the quadratic convergence of the complex HZ method for the positive definite generalized eigenvalue problem ⋮ On the Global Convergence of the Complex HZ Method ⋮ On the global convergence of the block Jacobi method for the positive definite generalized eigenvalue problem

Uses Software

• LAPACK
• ChASE

Cites Work

• Unnamed Item
• Orthosymmetric block reflectors
• Componentwise analysis of direct factorization of real symmetric and Hermitian matrices
• Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices
• Parallelization of the FLAPW method
• High-performance generation of the Hamiltonian and overlap matrices in FLAPW methods
• Block recursive algorithm to generate Jacobi-sets
• An implicit Jacobi-like method for computing generalized hyperbolic SVD
• Globally convergent Jacobi methods for positive definite matrix pairs
• Indefinite QR factorization
• A Hierarchically Blocked Jacobi SVD Algorithm for Single and Multiple Graphics Processing Units
• LAPACK Users' Guide
• Some Stable Methods for Calculating Inertia and Solving Symmetric Linear Systems
• Stable Subspace Tracking Algorithm Based on a Signed URV Decomposition
• On the Global Convergence of the Complex HZ Method
• ChASE
• Direct Methods for Solving Symmetric Indefinite Systems of Linear Equations

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