Random Krylov spaces over finite fields
Motivated by a connection with block iterative methods for solving linear systems over finite fields, we consider the probability that the Krylov space generated by a fixed linear mapping and a random set of elements in a vector space over a finite field equals the space itself. We obtain an exact f...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
2003
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| _version_ | 1797067843129311232 |
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| author | Brent, R Gao, S Lauder, A |
| author_facet | Brent, R Gao, S Lauder, A |
| author_sort | Brent, R |
| collection | OXFORD |
| description | Motivated by a connection with block iterative methods for solving linear systems over finite fields, we consider the probability that the Krylov space generated by a fixed linear mapping and a random set of elements in a vector space over a finite field equals the space itself. We obtain an exact formula for this probability and from it we derive good lower bounds that approach 1 exponentially fast as the size of the set increases. |
| first_indexed | 2024-03-06T22:02:10Z |
| format | Journal article |
| id | oxford-uuid:4ef81183-7baf-481b-9f62-4d1b7456ecb4 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:02:10Z |
| publishDate | 2003 |
| record_format | dspace |
| spelling | oxford-uuid:4ef81183-7baf-481b-9f62-4d1b7456ecb42022-03-26T16:04:24ZRandom Krylov spaces over finite fieldsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:4ef81183-7baf-481b-9f62-4d1b7456ecb4EnglishSymplectic Elements at Oxford2003Brent, RGao, SLauder, AMotivated by a connection with block iterative methods for solving linear systems over finite fields, we consider the probability that the Krylov space generated by a fixed linear mapping and a random set of elements in a vector space over a finite field equals the space itself. We obtain an exact formula for this probability and from it we derive good lower bounds that approach 1 exponentially fast as the size of the set increases. |
| spellingShingle | Brent, R Gao, S Lauder, A Random Krylov spaces over finite fields |
| title | Random Krylov spaces over finite fields |
| title_full | Random Krylov spaces over finite fields |
| title_fullStr | Random Krylov spaces over finite fields |
| title_full_unstemmed | Random Krylov spaces over finite fields |
| title_short | Random Krylov spaces over finite fields |
| title_sort | random krylov spaces over finite fields |
| work_keys_str_mv | AT brentr randomkrylovspacesoverfinitefields AT gaos randomkrylovspacesoverfinitefields AT laudera randomkrylovspacesoverfinitefields |