Fixed-point iterative linear inverse solver with extended precision
Abstract Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative solvers are carried out on floating-point processing units, which are not efficient in handling l...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Nature Portfolio
2023-03-01
|
| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-023-32338-5 |
| _version_ | 1797853951276613632 |
|---|---|
| author | Zheyuan Zhu Andrew B. Klein Guifang Li Sean Pang |
| author_facet | Zheyuan Zhu Andrew B. Klein Guifang Li Sean Pang |
| author_sort | Zheyuan Zhu |
| collection | DOAJ |
| description | Abstract Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative solvers are carried out on floating-point processing units, which are not efficient in handling large-scale matrix multiplications and inversions. Low-precision, fixed-point digital or analog processors consume only a fraction of the energy per operation than their floating-point counterparts, yet their current usages exclude iterative solvers due to the cumulative computational errors arising from fixed-point arithmetic. In this work, we show that for a simple iterative algorithm, such as Richardson iteration, using a fixed-point processor can provide the same convergence rate and achieve solutions beyond its native precision when combined with residual iteration. These results indicate that power-efficient computing platforms consisting of analog computing devices can be used to solve a broad range of problems without compromising the speed or precision. |
| first_indexed | 2024-04-09T19:57:59Z |
| format | Article |
| id | doaj.art-dc7af8b0a4dc4804aa2e30ef3d786630 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-04-09T19:57:59Z |
| publishDate | 2023-03-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-dc7af8b0a4dc4804aa2e30ef3d7866302023-04-03T05:22:17ZengNature PortfolioScientific Reports2045-23222023-03-0113111110.1038/s41598-023-32338-5Fixed-point iterative linear inverse solver with extended precisionZheyuan Zhu0Andrew B. Klein1Guifang Li2Sean Pang3CREOL, College of Optics and Photonics, University of Central FloridaCREOL, College of Optics and Photonics, University of Central FloridaCREOL, College of Optics and Photonics, University of Central FloridaCREOL, College of Optics and Photonics, University of Central FloridaAbstract Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative solvers are carried out on floating-point processing units, which are not efficient in handling large-scale matrix multiplications and inversions. Low-precision, fixed-point digital or analog processors consume only a fraction of the energy per operation than their floating-point counterparts, yet their current usages exclude iterative solvers due to the cumulative computational errors arising from fixed-point arithmetic. In this work, we show that for a simple iterative algorithm, such as Richardson iteration, using a fixed-point processor can provide the same convergence rate and achieve solutions beyond its native precision when combined with residual iteration. These results indicate that power-efficient computing platforms consisting of analog computing devices can be used to solve a broad range of problems without compromising the speed or precision.https://doi.org/10.1038/s41598-023-32338-5 |
| spellingShingle | Zheyuan Zhu Andrew B. Klein Guifang Li Sean Pang Fixed-point iterative linear inverse solver with extended precision Scientific Reports |
| title | Fixed-point iterative linear inverse solver with extended precision |
| title_full | Fixed-point iterative linear inverse solver with extended precision |
| title_fullStr | Fixed-point iterative linear inverse solver with extended precision |
| title_full_unstemmed | Fixed-point iterative linear inverse solver with extended precision |
| title_short | Fixed-point iterative linear inverse solver with extended precision |
| title_sort | fixed point iterative linear inverse solver with extended precision |
| url | https://doi.org/10.1038/s41598-023-32338-5 |
| work_keys_str_mv | AT zheyuanzhu fixedpointiterativelinearinversesolverwithextendedprecision AT andrewbklein fixedpointiterativelinearinversesolverwithextendedprecision AT guifangli fixedpointiterativelinearinversesolverwithextendedprecision AT seanpang fixedpointiterativelinearinversesolverwithextendedprecision |