@book{Bellman1957,
  author    = {Richard Bellman},
  title     = {Dynamic Programming},
  publisher = {Princeton University Press},
  address   = {Princeton, NJ},
  year      = {1957}
}

@book{GolubVanLoan2013,
  author    = {Gene H. Golub and Charles F. Van Loan},
  title     = {Matrix Computations},
  edition   = {Fourth},
  publisher = {Johns Hopkins University Press},
  address   = {Baltimore, MD},
  year      = {2013}
}

@book{Higham2002,
  author    = {Nicholas J. Higham},
  title     = {Accuracy and Stability of Numerical Algorithms},
  edition   = {Second},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia, PA},
  year      = {2002},
  doi       = {10.1137/1.9780898718027}
}

@book{Saad2003,
  author    = {Yousef Saad},
  title     = {Iterative Methods for Sparse Linear Systems},
  edition   = {Second},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia, PA},
  year      = {2003},
  doi       = {10.1137/1.9780898718003}
}

@book{Davis2006,
  author    = {Timothy A. Davis},
  title     = {Direct Methods for Sparse Linear Systems},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia, PA},
  year      = {2006},
  doi       = {10.1137/1.9780898718881}
}

@article{Hager1989,
  author  = {William W. Hager},
  title   = {Updating the Inverse of a Matrix},
  journal = {SIAM Review},
  volume  = {31},
  number  = {2},
  pages   = {221--239},
  year    = {1989},
  doi     = {10.1137/1031049}
}

@article{EckartYoung1936,
  author  = {Carl Eckart and Gale Young},
  title   = {The Approximation of One Matrix by Another of Lower Rank},
  journal = {Psychometrika},
  volume  = {1},
  number  = {3},
  pages   = {211--218},
  year    = {1936},
  doi     = {10.1007/BF02288367}
}

@article{Mirsky1960,
  author  = {Leon Mirsky},
  title   = {Symmetric Gauge Functions and Unitarily Invariant Norms},
  journal = {The Quarterly Journal of Mathematics},
  series  = {2},
  volume  = {11},
  pages   = {50--59},
  year    = {1960},
  doi     = {10.1093/qmath/11.1.50}
}

@article{BunchNielsen1978,
  author  = {James R. Bunch and Christopher P. Nielsen},
  title   = {Updating the Singular Value Decomposition},
  journal = {Numerische Mathematik},
  volume  = {31},
  pages   = {111--129},
  year    = {1978},
  doi     = {10.1007/BF01397471}
}

@article{GolubKahan1965,
  author  = {Gene H. Golub and William Kahan},
  title   = {Calculating the Singular Values and Pseudo Inverse of a Matrix},
  journal = {Journal of the Society for Industrial and Applied Mathematics, Series B: Numerical Analysis},
  volume  = {2},
  number  = {2},
  pages   = {205--224},
  year    = {1965},
  doi     = {10.1137/0702016}
}

@article{CoifmanWickerhauser1992,
  author  = {Ronald R. Coifman and Mladen Victor Wickerhauser},
  title   = {Entropy Based Algorithms for Best Basis Selection},
  journal = {IEEE Transactions on Information Theory},
  volume  = {38},
  number  = {2},
  pages   = {713--718},
  year    = {1992},
  doi     = {10.1109/18.119732}
}

@inproceedings{HongKung1981,
  author    = {Jia Wei Hong and H. T. Kung},
  title     = {I O Complexity: The Red Blue Pebble Game},
  booktitle = {Proceedings of the Thirteenth Annual ACM Symposium on Theory of Computing},
  pages     = {326--333},
  publisher = {Association for Computing Machinery},
  year      = {1981},
  doi       = {10.1145/800076.802486}
}

@article{WilliamsWatermanPatterson2009,
  author  = {Samuel Williams and Andrew Waterman and David Patterson},
  title   = {Roofline: An Insightful Visual Performance Model for Multicore Architectures},
  journal = {Communications of the ACM},
  volume  = {52},
  number  = {4},
  pages   = {65--76},
  year    = {2009},
  doi     = {10.1145/1498765.1498785}
}

@article{BallardDemmelHoltzSchwartz2011,
  author  = {Grey Ballard and James Demmel and Olga Holtz and Oded Schwartz},
  title   = {Minimizing Communication in Numerical Linear Algebra},
  journal = {SIAM Journal on Matrix Analysis and Applications},
  volume  = {32},
  number  = {3},
  pages   = {866--901},
  year    = {2011},
  doi     = {10.1137/090769156}
}

@article{HalkoMartinssonTropp2011,
  author  = {Nathan Halko and Per Gunnar Martinsson and Joel A. Tropp},
  title   = {Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions},
  journal = {SIAM Review},
  volume  = {53},
  number  = {2},
  pages   = {217--288},
  year    = {2011},
  doi     = {10.1137/090771806}
}

@article{MartinssonTropp2020,
  author  = {Per Gunnar Martinsson and Joel A. Tropp},
  title   = {Randomized Numerical Linear Algebra: Foundations and Algorithms},
  journal = {Acta Numerica},
  volume  = {29},
  pages   = {403--572},
  year    = {2020},
  doi     = {10.1017/S0962492920000021}
}

@article{DavisKahan1970,
  author  = {Chandler Davis and William M. Kahan},
  title   = {The Rotation of Eigenvectors by a Perturbation. III},
  journal = {SIAM Journal on Numerical Analysis},
  volume  = {7},
  number  = {1},
  pages   = {1--46},
  year    = {1970},
  doi     = {10.1137/0707001}
}

@article{CarsonHigham2018,
  author  = {Erin Carson and Nicholas J. Higham},
  title   = {Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions},
  journal = {SIAM Journal on Scientific Computing},
  volume  = {40},
  number  = {2},
  pages   = {A817--A847},
  year    = {2018},
  doi     = {10.1137/17M1140819}
}

@article{Strassen1969,
  author  = {Volker Strassen},
  title   = {Gaussian Elimination Is Not Optimal},
  journal = {Numerische Mathematik},
  volume  = {13},
  pages   = {354--356},
  year    = {1969},
  doi     = {10.1007/BF02165411}
}

@article{DemmelHoltzSchwartz2007,
  author  = {James Demmel and Ioana Dumitriu and Olga Holtz},
  title   = {Fast Linear Algebra Is Stable},
  journal = {Numerische Mathematik},
  volume  = {108},
  number  = {1},
  pages   = {59--91},
  year    = {2007},
  doi     = {10.1007/s00211-007-0114-x}
}

@article{AmbikasaranDarve2013,
  author  = {Sivaram Ambikasaran and Eric Darve},
  title   = {An O N Log N Fast Direct Solver for Partial Hierarchically Semi Separable Matrices},
  journal = {Journal of Scientific Computing},
  volume  = {57},
  number  = {3},
  pages   = {477--501},
  year    = {2013},
  doi     = {10.1007/s10915-013-9714-z}
}

@article{CooleyTukey1965,
  author  = {James W. Cooley and John W. Tukey},
  title   = {An Algorithm for the Machine Calculation of Complex Fourier Series},
  journal = {Mathematics of Computation},
  volume  = {19},
  number  = {90},
  pages   = {297--301},
  year    = {1965},
  doi     = {10.1090/S0025-5718-1965-0178586-1}
}

@article{Oseledets2011,
  author  = {Ivan V. Oseledets},
  title   = {Tensor Train Decomposition},
  journal = {SIAM Journal on Scientific Computing},
  volume  = {33},
  number  = {5},
  pages   = {2295--2317},
  year    = {2011},
  doi     = {10.1137/090752286}
}

@inproceedings{FrigoLeisersonProkopRamachandran1999,
  author    = {Matteo Frigo and Charles E. Leiserson and Harald Prokop and Sridhar Ramachandran},
  title     = {Cache Oblivious Algorithms},
  booktitle = {Proceedings of the Fortieth Annual Symposium on Foundations of Computer Science},
  pages     = {285--297},
  publisher = {IEEE Computer Society},
  year      = {1999},
  doi       = {10.1109/SFFCS.1999.814600}
}

@manual{NVIDIA2026,
  author       = {{NVIDIA Corporation}},
  title        = {CUDA C++ Programming Guide},
  organization = {NVIDIA Corporation},
  note         = {Archive version 12.8.1, Section 3.2.8.7 (CUDA Graphs), accessed 6 October 2026},
  url          = {https://docs.nvidia.com/cuda/archive/12.8.1/cuda-c-programming-guide/index.html#cuda-graphs}
}

@misc{IEEE7542019,
  author       = {{IEEE Standards Association}},
  title        = {IEEE Standard for Floating Point Arithmetic},
  howpublished = {IEEE Std 754 2019},
  year         = {2019},
  doi          = {10.1109/IEEESTD.2019.8766229}
}

@misc{HighamMary2021,
  author = {Higham, Nicholas J. and Mary, Theo},
  title = {Mixed Precision Algorithms in Numerical Linear Algebra},
  year = {2021},
  note = {MIMS EPrint 2021.20, Sections 3--4; classical real dot-product forward-error model},
  url = {https://eprints.maths.manchester.ac.uk/2841/1/paper_eprint.pdf}
}