Geodesic
Conjugate direction methods for multiple solution of SLAEs
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 26-42

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Conjugate gradient and conjugate residual methods for multiple solution of systems of linear algebraic equations (SLAE) with the same matrices but with different successively determined right-hand sides are considered. In order to speed up the iterative processes when solving the second and subsequent SLAEs, deflation algorithms are applied. These algorithms use the direction vectors obtained in the course of solving the first system as the basis vectors. Results of numerical experiments for model examples, illustrating the efficiency of the approaches under consideration, are provided. 
@article{ZNSL_2020_496_a1,
     author = {Y. L. Gurieva and V. P. Il'in},
     title = {Conjugate direction methods for multiple solution of {SLAEs}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {26--42},
     publisher = {mathdoc},
     volume = {496},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a1/}
}
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Y. L. Gurieva; V. P. Il'in. Conjugate direction methods for multiple solution of SLAEs. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXIII, Tome 496 (2020), pp. 26-42. http://geodesic.mathdoc.fr/item/ZNSL_2020_496_a1/