On BLAS Level-3 Implementations of Common Solvers for (Quasi-) Triangular Generalized Lyapunov Equations

DOI10.1145/2850415zbMath1371.65040OpenAlexW2509884827WikidataQ113310210 ScholiaQ113310210MaRDI QIDQ5270766

Martin Köhler, Jens Saak

Publication date: 30 June 2017

Published in: ACM Transactions on Mathematical Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1145/2850415

zbMATH Keywords

algorithmLyapunov equationBartels-Stewart algorithmmatrix equationsSylvester equationblocked algorithmBLAS level-3

Mathematics Subject Classification ID

Matrix equations and identities (15A24) Parallel numerical computation (65Y05)

Related Items (max. 100)

Recursive blocked algorithms for linear systems with Kronecker product structure

Uses Software

• SLICOT
• SCASY
• mctoolbox
• MKL
• CTLEX
• Algorithm 432

Cites Work

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• mctoolbox
• The solution of the matrix equations \(AXB-CXD=E\) and \((YA-DZ,YC- BZ)=(E,F)\)
• Numerical solution of generalized Lyapunov equations
• A Parallel QZ Algorithm for Distributed Memory HPC Systems
• Parallel Solvers for Sylvester-Type Matrix Equations with Applications in Condition Estimation, Part I
• Algorithm 904
• Principal component analysis in linear systems: Controllability, observability, and model reduction
• Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
• Generalized Schur methods with condition estimators for solving the generalized Sylvester equation
• LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs
• Solution of the Sylvester matrix equation AXB ^T + CXD ^T = E
• Accuracy and Stability of Numerical Algorithms
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• Multishift Variants of the QZ Algorithm with Aggressive Early Deflation
• Recursive blocked algorithms for solving triangular systems—Part I
• Recursive blocked algorithms for solving triangular systems—Part II
• An Algorithm for Generalized Matrix Eigenvalue Problems

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