譜圖論

== 沿革 ==

== 沿革 ==

譜圖論在1950年代至1960年代逐漸出現。[[图论]]有研究圖的結構與譜性質之間有何聯繫，除此之外，[[量子化学]]研究亦是另一源頭，但兩個方向的研究互不流通，要到很後期才合而為一。<ref name= cvet2>{{cite book |title = Eigenspaces of Graphs| trans-title = 圖之本徵空間|first1 = Dragoš |last1 = Cvetković|first2= Peter |last2 = Rowlinson|first3 = Slobodan|last3 = Simić|year = 1997 |isbn = 0-521-57352-1|publisher = [[Cambridge University Press]]|doi = 10.1017/CBO9781139086547}}</ref>1980年茨維特科維奇<!–沿用[[德拉吉莎·茨維特科維奇]]姓的譯法–>、杜布<!–沿用[[鞅 (概率論)]]中Joseph L. Doob姓的譯法–>、薩克斯的專著《圖之譜》<ref>{{cite book| first1 = Dragoš M.|last1 = Cvetković| first2 = Michael|last2 = Doob|first3 = Horst|last3 = Sachs|title = Spectra of Graphs| trans-title = 圖之譜 |year = 1980|location = New York |publisher = Academic Press|language = en}}</ref>概括了當時本領域的多數研究，其後由1988年《圖譜論之近期成果》<ref>{{cite book|first1=Dragoš M.|last1=Cvetković |first2=Michael |last2=Doob |first3=Ivan |last3=Gutman |first4=A. |last4=Torgasev |title=Recent Results in the Theory of Graph Spectra |trans-title = 圖譜論之近期成果|series=Annals of Discrete mathematics |number=36 |year=1988 |isbn=0-444-70361-6 |url=http://www.sciencedirect.com/science/bookseries/01675060/36 |doi = 10.1016/s0167-5060(08)x7010-4|volume = 36}}</ref>和《圖之譜》1995年第三版再次更新。<ref name= cvet2/>2000年代，{{link-en|砂田利一|Toshikazu Sunada}}開創離散幾何分析，並加以發展。此領域處理譜圖論的方式，是利用加權圖的離散拉氏算子，<ref>{{cite journal | last = Sunada | first = Toshikazu | journal = Proceedings of Symposia in Pure Mathematics | pages = 51–86 | title = Discrete geometric analysis |trans-title = 離散幾何分析| volume = 77 | year = 2008| doi = 10.1090/pspum/077/2459864 | isbn = 9780821844717 }}</ref>在{{link-en|譜形分析|Spectral shape analysis|形狀分析}}等領域有應用。近來，譜圖論應用廣泛，用於分析一些現實（如信號處理時）可能會遇到的<!–英文此處有vertex-varying，未能理解–>圖。<ref>{{Cite journal|last=Shuman|first=David I|last2=Ricaud|first2=Benjamin|last3=Vandergheynst|first3=Pierre|date=March 2016|title=Vertex-frequency analysis on graphs|trans-title = 圖上的頂點頻率分析|journal=Applied and Computational Harmonic Analysis|volume=40|issue=2|pages=260–291|doi=10.1016/j.acha.2015.02.005|issn=1063-5203|arxiv=1307.5708|language = en}}</ref><ref>{{Cite journal|last=Stankovic|first=Ljubisa|last2=Dakovic|first2=Milos|last3=Sejdic|first3=Ervin|date=July 2017|title=Vertex-Frequency Analysis: A Way to Localize Graph Spectral Components [Lecture Notes]|trans-title = 頂點頻率分析：局部化圖譜分量的方法 [講義]|journal=IEEE Signal Processing Magazine|language=en|volume=34|issue=4|pages=176–182|doi=10.1109/msp.2017.2696572|issn=1053-5888|bibcode=2017ISPM…34..176S}}</ref><ref>{{Cite journal|last=Sakiyama|first=Akie|last2=Watanabe|first2=Kana|last3=Tanaka|first3=Yuichi|date=September 2016|title=Spectral Graph Wavelets and Filter Banks With Low Approximation Error|trans-title = 譜圖小波和低近似誤差的濾波器組|journal=IEEE Transactions on Signal and Information Processing over Networks|language=en|volume=2|issue=3|pages=230–245|doi=10.1109/tsipn.2016.2581303|issn=2373-776X}}</ref><ref>{{Cite journal|last=Behjat|first=Hamid|last2=Richter|first2=Ulrike|last3=Van De Ville|first3=Dimitri|last4=Sornmo|first4=Leif|date=2016-11-15|title=Signal-Adapted Tight Frames on Graphs |trans-title = 圖上適應訊號的緊標架|journal=IEEE Transactions on Signal Processing|volume=64|issue=22|pages=6017–6029|doi=10.1109/tsp.2016.2591513|issn=1053-587X|bibcode=2016ITSP…64.6017B|url=http://infoscience.epfl.ch/record/223159|language = en}}</ref>

== 參見 ==

== 參見 ==