Low-rank tensor methods for Markov chains with applications to tumor progression models
DOI10.1007/s00285-022-01846-9zbMath1505.92046arXiv2006.08135OpenAlexW3035705467MaRDI QIDQ2105306
Peter Georg, Tilo Wettig, Rainer Spang, Rudolf Schill, Maren Klever, Lars Grasedyck
Publication date: 8 December 2022
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2006.08135
Computational methods in Markov chains (60J22) Applications of continuous-time Markov processes on discrete state spaces (60J28) Numerical methods for low-rank matrix approximation; matrix compression (65F55) Pathology, pathophysiology (92C32)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Product-form stationary distributions for deficiency zero chemical reaction networks
- Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework
- Approximate iterations for structured matrices
- Iterative methods for overflow queueing models. I
- Approximating the inverse of a matrix for use in iterative algorithms on vector processors
- Compact representation of solution vectors in Kronecker-based Markovian analysis
- Multigrid methods combined with low-rank approximation for tensor-structured Markov chains
- A new scheme for the tensor representation
- An introduction to hierarchical (\(\mathcal H\)-) rank and TT-rank of tensors with examples
- Analysis of individual differences in multidimensional scaling via an \(n\)-way generalization of ``Eckart-Young decomposition
- A literature survey of low-rank tensor approximation techniques
- Hierarchical Singular Value Decomposition of Tensors
- Tensor Spaces and Numerical Tensor Calculus
- Distributed hierarchical SVD in the Hierarchical Tucker format
- Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
- Markov models for accumulating mutations
- On the Convergence of a Class of Multilevel Methods for Large Sparse Markov Chains
- Product Form Steady-State Distribution for Stochastic Automata Networks with Domino Synchronizations
- Introduction to Modeling and Analysis of Stochastic Systems
- Computer-Oriented Formulation of Transition-Rate Matrices via Kronecker Algebra
- Algorithm 941
- Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
- The Spacey Random Walk: A Stochastic Process for Higher-Order Data
This page was built for publication: Low-rank tensor methods for Markov chains with applications to tumor progression models