This webpage is dedicated to the
RankFactorizationProblem (click
here)
package dedicated to the effective study
of the rank factorization problem.
The rank factorization problem aims at solving the following problem: Let K be a field,
M ∈ K^{m × n}, and D_{1}, ..., D_{r} ∈ K^{m ×
m}, find a column vector u ∈ K^{m × 1} and r row
vectors v_{1}, ..., v_{r} ∈ K^{1 ×
n} such that M =
D_{1} u v_{1} + ... + D_{r} u v_{r}.
This rank factorization problem arises in gearbox vibration analysis as a demodulation
problem. For more details, see:
Elisa Hubert,
Amplitude and phase demodulation of multicarrier signals: Application to gear vibration signals, PhD thesis, University of Lyon, France, 2019.
This problem was studied in:

Hubert, E., Barrau, A., Badaoui, M. E., "New multicarrier
demodulation method applied to gearbox vibration analysis", Proceedings of ICASSP, 2018.

Hubert, E.,
Amplitude and phase demodulation of multicarrier signals: Application to gear vibration signals, PhD thesis, University of Lyon, France, 2019.

Hubert, E., Bouzidi, Y., Dagher, R., Barrau, A., Quadrat, A. (2019). "Algebraic
aspects of the exact signal demodulation problem", Proceedings of SSSC & TDS
, Sinaia (Romania), 0911/09/2019 (
paper.pdf
).

Hubert, E., Barrau, A., Bouzidi, Y., Dagher, R., Quadrat,
A. (2020). "On a rank factorisation problem arising in gearbox
vibration analysis", Proceedings of the
21st IFAC World Congress
, Germany, 1217/07/2020 (
paper.pdf
).

Hubert, E., Bouzidi, Y., Dagher, R., Quadrat,
A. (2021). "Centrohermitian solutions of a factorization problem
arising in vibration analysis. Part I: Lee's transformation", Proceedings of the
European Control Conference 2021
(
paper.pdf
).

Hubert, E., Bouzidi, Y., Dagher, R., Quadrat,
A. (2021). "Centrohermitian solutions of a factorization problem
arising in vibration analysis. Part II: A coninvolutory matrix
approach", Proceedings of the
European Control Conference 2021
(
paper.pdf
).

Hubert, E., Bouzidi, Y., Dagher, R., Quadrat,
A. (2021). "Algebraic aspects of a rank factorization problem
arising in vibration analysis", Maple in Mathematics Education and
Research, Communications in Computer and Information Science, vol.
1414, Springer, 104118 (
paper.pdf
, Maple and pdf files of the
examples).

Dagher, R., Hubert, E., Quadrat,
A. (2023). "On the general solutions of a rank factorization problem
arising in vibration analysis",
INRIA Research Report n. 9438, submitted for publication (
Inria Report 9438).
For an example handled by
CapAndHomalg
(GAP), see Appendix of:
Dagher, R., Hubert, E., Quadrat,
A. (2021). "On the general solutions of a rank factorization problem
arising in vibration analysis",
INRIA Research Report n. 9438, version 1
(
Inria Report 9438).
The corresponding CapAndHomalg file can be downloaded here
RR9438.ipynb
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