DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | Ziegler, Martin | - |
dc.contributor.advisor | 마틴 지글러 | - |
dc.contributor.author | Koswara, Ivan Adrian | - |
dc.date.accessioned | 2022-04-27T19:31:55Z | - |
dc.date.available | 2022-04-27T19:31:55Z | - |
dc.date.issued | 2021 | - |
dc.identifier.uri | http://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=948475&flag=dissertation | en_US |
dc.identifier.uri | http://hdl.handle.net/10203/296109 | - |
dc.description | 학위논문(석사) - 한국과학기술원 : 전산학부, 2021.2,[i, 30 p. :] | - |
dc.description.abstract | Exponential-size problems have not been investigated very well in complexity theory even though they appear in several applications. For example, approximating the solution of a partial differential equation requires one to raise an exponential-size matrix to a large power. We formally define linear algebra problems when the input vectors and matrices have size that is exponential in a parameter and have real number entries. We also investigate the computational complexity of these problems. We show that computing exponential-size inner product is in $\#\mathsf{P}$ and computing exponential-size matrix powering is in $\mathsf{FPSPACE}$, and these are both optimal. Furthermore, inspired from the partial differential equation motivation, we show some matrices can be converted into polynomials, and that computing polynomial powering is in $\#\mathsf{P}$, improving the matrix powering result for these matrices. We also show that some cases of polynomial powering are in $\mathsf{FP}$ with novel methods, and computing (not exponential-size) inner product and matrix powering can be done in sublinear space. | - |
dc.language | eng | - |
dc.publisher | 한국과학기술원 | - |
dc.subject | Computational complexity▼aExponential-size problem▼aExact real computation | - |
dc.subject | 계산복잡도▼a지수 크기 문제▼a정확한 실수 계산 | - |
dc.title | Computational complexity of linear algebra problems with exponential size and real entries | - |
dc.title.alternative | 실수에서의 지수 크기 선형대수학 문제의 계산 복잡도 | - |
dc.type | Thesis(Master) | - |
dc.identifier.CNRN | 325007 | - |
dc.description.department | 한국과학기술원 :전산학부, | - |
dc.contributor.alternativeauthor | 코스아라 이반 아드리안 | - |
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