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A Riemannian Optimization Approach for Computing Low-Rank Solutions of Lyapunov Equations

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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

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Existence of a low rank or ℋ‐matrix approximant to the solution of a Sylvester equation
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A variance propagation algorithm for stochastic heat and mass transfer problems in food processes
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HSL_MI20: An efficient AMG preconditioner for finite element problems in 3D
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Efficient numerical solution of the LQR‐problem for the heat equation
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Optimization and Dynamical Systems
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A Parameter Free ADI-Like Method for the Numerical Solution of Large Scale Lyapunov Equations
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A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization
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Newton methods for nonsmooth convex minimization: connections among -Lagrangian, Riemannian Newton and SQP methods
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Trust-Region Methods on Riemannian Manifolds
inferredcites →https://doi.org/10.1016/0024-3795(93)00070-gopenalex-snapshot
Critical points of matrix least squares distance functions
inferredcites →https://doi.org/10.1016/j.laa.2004.11.004openalex-snapshot
Projection methods for large Lyapunov matrix equations
inferredcites →https://doi.org/10.1016/s0024-3795(87)90314-4openalex-snapshot
The solution of the matrix equations AXB−CXD=E AND (YA−DZ,YC−BZ)=(E,F)
inferredcites →https://doi.org/10.1016/s0079-8169(08)x6065-9openalex-snapshot
An Introduction to Differentiable Manifolds and Riemannian Geometry
inferredcites →https://doi.org/10.1016/s0167-6911(00)00010-4openalex-snapshot
Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
inferredcites →https://doi.org/10.1016/s0167-6911(02)00147-0openalex-snapshot
On the decay rate of Hankel singular values and related issues
inferredcites →https://doi.org/10.1016/s0377-0427(00)00393-9openalex-snapshot
The ubiquitous Kronecker product
inferredcites →https://doi.org/10.1017/9781108993456.011openalex-snapshot
Numerical optimization
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Topics in Matrix Analysis
inferredcites →https://doi.org/10.1017/s0962492904000212openalex-snapshot
Numerical solution of saddle point problems
inferredcites →https://doi.org/10.1023/a:1018979826766openalex-snapshot
Numerical solution of generalized Lyapunov equations
inferredcites →https://doi.org/10.1023/a:1022205420182openalex-snapshot
A Modified Low-Rank Smith Method for Large-Scale Lyapunov Equations
inferredcites →https://doi.org/10.1109/tac.1981.1102568openalex-snapshot
Principal component analysis in linear systems: Controllability, observability, and model reduction
inferredcites →https://doi.org/10.1137/040618102openalex-snapshot
A Multigrid Method to Solve Large Scale Sylvester Equations
inferredcites →https://doi.org/10.1137/050639703openalex-snapshot
Dynamical Low‐Rank Approximation
inferredcites →https://doi.org/10.1137/06066120xopenalex-snapshot
A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
inferredcites →https://doi.org/10.1137/0720042openalex-snapshot
The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
inferredcites →https://doi.org/10.1137/0731012openalex-snapshot
Krylov Subspace Methods for Solving Large Lyapunov Equations
inferredcites →https://doi.org/10.1137/080731359openalex-snapshot
Low-Rank Optimization on the Cone of Positive Semidefinite Matrices
inferredcites →https://doi.org/10.1137/090756843openalex-snapshot
Krylov Subspace Methods for Linear Systems with Tensor Product Structure
inferredcites →https://doi.org/10.1137/1.9780898718713openalex-snapshot
Approximation of Large-Scale Dynamical Systems
inferredcites →https://doi.org/10.1137/1.9780898719857openalex-snapshot
Trust Region Methods
inferredcites →https://doi.org/10.1137/1012104openalex-snapshot
Explicit Solutions of Linear Matrix Equations
inferredcites →https://doi.org/10.1137/s0036144504443389openalex-snapshot
Low-Rank Solution of Lyapunov Equations
inferredcites →https://doi.org/10.1137/s0895479895290954openalex-snapshot
The Geometry of Algorithms with Orthogonality Constraints
inferredcites →https://doi.org/10.1137/s1052623497322735openalex-snapshot
Solving the Trust-Region Subproblem using the Lanczos Method
inferredcites →https://doi.org/10.1137/s1064827598347666openalex-snapshot
A Cyclic Low-Rank Smith Method for Large Sparse Lyapunov Equations
inferredcites →https://doi.org/10.1145/1391989.1391995openalex-snapshot
Algorithm 887
inferredcites →https://doi.org/10.1145/361573.361582openalex-snapshot
Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
inferredcites →https://doi.org/10.1162/neco.2008.04-08-749openalex-snapshot
A Geometric Newton Method for Oja's Vector Field
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Alternating Projections on Manifolds
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Optimization Algorithms on Matrix Manifolds
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Sparse Matrices and Their Uses.
inferredcites →https://doi.org/10.56021/9781421407944openalex-snapshot
Matrix Computations

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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Some Explicit Solutions and Bounds to the Generalized Lyapunov Matrix Inequality
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