Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning
<p dir="ltr">Hardware trends have motivated the development of mixed precision algorithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive precision sparse matrix–vector produce...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | |
| Published: |
2025
|
| Subjects: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1864513525518434304 |
|---|---|
| author | Noaman Khan (19810050) |
| author2 | Erin Carson (22928818) |
| author2_role | author |
| author_facet | Noaman Khan (19810050) Erin Carson (22928818) |
| author_role | author |
| dc.creator.none.fl_str_mv | Noaman Khan (19810050) Erin Carson (22928818) |
| dc.date.none.fl_str_mv | 2025-08-14T09:00:00Z |
| dc.identifier.none.fl_str_mv | 10.1007/s00366-025-02187-z |
| dc.relation.none.fl_str_mv | https://figshare.com/articles/journal_contribution/Mixed_precision_iterative_refinement_with_adaptive_precision_sparse_approximate_inverse_preconditioning/30971590 |
| dc.rights.none.fl_str_mv | CC BY 4.0 info:eu-repo/semantics/openAccess |
| dc.subject.none.fl_str_mv | Information and computing sciences Theory of computation Mathematical sciences Applied mathematics Matrix computations Mixed precision Numerical linear algebra Linear systems Adaptive algorithms |
| dc.title.none.fl_str_mv | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning |
| dc.type.none.fl_str_mv | Text Journal contribution info:eu-repo/semantics/publishedVersion text contribution to journal |
| description | <p dir="ltr">Hardware trends have motivated the development of mixed precision algorithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive precision sparse matrix–vector produce routine, which may be used to accelerate the solution of sparse linear systems by iterative methods. This approach is also applicable to the application of inexact preconditioners, such as sparse approximate inverse preconditioners used in Krylov subspace methods. In this work, we develop an adaptive precision sparse approximate inverse preconditioner and demonstrate its use within a five-precision GMRES-based iterative refinement method. We call this algorithm variant BSPAI-GMRES-IR. We then analyze the conditions for the convergence of BSPAI-GMRES-IR, and determine settings under which BSPAI-GMRES-IR will produce similar backward and forward errors as the existing SPAI-GMRES-IR method, the latter of which does not use adaptive precision in preconditioning. Our numerical experiments show that this approach can potentially lead to a reduction in the cost of storing and applying sparse approximate inverse preconditioners, although a significant reduction in cost may comes at the expense of increasing the number of GMRES iterations required for convergence.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Engineering with Computers<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1007/s00366-025-02187-z" target="_blank">https://dx.doi.org/10.1007/s00366-025-02187-z</a></p> |
| eu_rights_str_mv | openAccess |
| id | Manara2_2e1a2a573cf11c2f2822fcd5fe8be511 |
| identifier_str_mv | 10.1007/s00366-025-02187-z |
| network_acronym_str | Manara2 |
| network_name_str | Manara2 |
| oai_identifier_str | oai:figshare.com:article/30971590 |
| publishDate | 2025 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| rights_invalid_str_mv | CC BY 4.0 |
| spelling | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioningNoaman Khan (19810050)Erin Carson (22928818)Information and computing sciencesTheory of computationMathematical sciencesApplied mathematicsMatrix computationsMixed precisionNumerical linear algebraLinear systemsAdaptive algorithms<p dir="ltr">Hardware trends have motivated the development of mixed precision algorithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive precision sparse matrix–vector produce routine, which may be used to accelerate the solution of sparse linear systems by iterative methods. This approach is also applicable to the application of inexact preconditioners, such as sparse approximate inverse preconditioners used in Krylov subspace methods. In this work, we develop an adaptive precision sparse approximate inverse preconditioner and demonstrate its use within a five-precision GMRES-based iterative refinement method. We call this algorithm variant BSPAI-GMRES-IR. We then analyze the conditions for the convergence of BSPAI-GMRES-IR, and determine settings under which BSPAI-GMRES-IR will produce similar backward and forward errors as the existing SPAI-GMRES-IR method, the latter of which does not use adaptive precision in preconditioning. Our numerical experiments show that this approach can potentially lead to a reduction in the cost of storing and applying sparse approximate inverse preconditioners, although a significant reduction in cost may comes at the expense of increasing the number of GMRES iterations required for convergence.</p><h2 dir="ltr">Other Information</h2><p dir="ltr">Published in: Engineering with Computers<br>License: <a href="https://creativecommons.org/licenses/by/4.0" target="_blank">https://creativecommons.org/licenses/by/4.0</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.1007/s00366-025-02187-z" target="_blank">https://dx.doi.org/10.1007/s00366-025-02187-z</a></p>2025-08-14T09:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.1007/s00366-025-02187-zhttps://figshare.com/articles/journal_contribution/Mixed_precision_iterative_refinement_with_adaptive_precision_sparse_approximate_inverse_preconditioning/30971590CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/309715902025-08-14T09:00:00Z |
| spellingShingle | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning Noaman Khan (19810050) Information and computing sciences Theory of computation Mathematical sciences Applied mathematics Matrix computations Mixed precision Numerical linear algebra Linear systems Adaptive algorithms |
| status_str | publishedVersion |
| title | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning |
| title_full | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning |
| title_fullStr | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning |
| title_full_unstemmed | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning |
| title_short | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning |
| title_sort | Mixed precision iterative refinement with adaptive precision sparse approximate inverse preconditioning |
| topic | Information and computing sciences Theory of computation Mathematical sciences Applied mathematics Matrix computations Mixed precision Numerical linear algebra Linear systems Adaptive algorithms |