Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences最新文献_第4页

The Factorization of a Matrix as the Commutator of Two Matrices 一个矩阵作为两个矩阵的对易子的分解

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI: 10.6028/JRES.078B.017

J. M. Smith

引用次数: 0

Computation of the field of values of a 2 x 2 matrix 2 × 2矩阵的值域的计算

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI: 10.6028/JRES.078B.016

Charles R. Johnson

引用次数: 6

Complete elliptic integrals resulting from infinite integrals of Bessel functions .II. 由贝塞尔函数的无穷积分得到完全椭圆积分。

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI: 10.6028/JRES.078B.018

S. Okui

引用次数: 11

How bad is Hadamard determinantal bound 哈达玛行列式界有多糟糕

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI: 10.6028/JRES.078B.021

Charles R. Johnson, M. Newman

引用次数: 5

The convex hull of transposition matrices 置换矩阵的凸包

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI: 10.6028/JRES.078B.019

L. S. Joel

{"title":"The convex hull of transposition matrices","authors":"L. S. Joel","doi":"10.6028/JRES.078B.019","DOIUrl":"https://doi.org/10.6028/JRES.078B.019","url":null,"abstract":"Many combinatorial optimization proble ms can be expressed as requiring the ex tre mization of a linear fun ction over some finite set S of points in a real N-dime nsion al space. To bring the theoretical and computational resources of linear programming to bear, it is necessary to cha racterize the convex hull K (S) of S as the solutio n-set of a \" ni cely structured\" family of linear inequalities and equations. The outs tanding example , arising in connec ti on with the assignment prob le m of operations research , has S = S\", the se t of n by n permutation matrices (regarded as points in n2 dim ension rll s pace). Here a we ll-known theore m I (Birkhoff-Hoffman-vo n Ne umann -W ielan dt et al.) identifies K (5,,) as the set of all n by n doubly stochasti c matrices X = (Xi), i.e. matrices with nonnegative e ntries and with e ach row and column summing to 1. It is expected th at a si milar cl 'aracte r ization of K ( Cn ), where Cll is the set of all cyclic permutation matrices, would be va lua ble in connection with the travelin g saleman proble m, but no such c harac teri zation has been given as ye t. For a given n le t TIc(l ~ c ~ n) de note the se t of n by n permutation matrices for which the decomposition of the associated perm utation into di sjoin t cycles conta in s exactly c cycles (i ncl udin g cycles of le ngth o ne). Sin ce Cn = TIl , the re mark endi ng the last paragraph suggests lookin g at th e \"other e nd\" of th e seque nce {nc}~= I' The situ ations for TIn and TInI are simp le, a nd form the s ubject of thi s note. Clearly TIll consists of the identity matrix In, so that K (TI,,) = {JII}' We go on to characterize K CTIn l ) as well as K(TIn1 U TI,, ) = K(TIn 1 U { In}) . Note that llll I consists of the n(n -1)/2 transposition matrices Tpq(l ~ p < q ~ n) defined by","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1974-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129391818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computational experience with an algorithm for finding the k shortest paths in a network 在网络中寻找k条最短路径的算法的计算经验

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI: 10.6028/JRES.078B.020

D. Shier

{"title":"Computational experience with an algorithm for finding the k shortest paths in a network","authors":"D. Shier","doi":"10.6028/JRES.078B.020","DOIUrl":"https://doi.org/10.6028/JRES.078B.020","url":null,"abstract":"A common task which arises In analyzing a system of interconnec ted elements or network is that of calculating shortest paths i. e., routes through the sys tem whose total le ngth or cos t is as small as possible_ Such calc ulations occur quite naturally in the context of trans portation and communication networks_ In applications s uch as these, it is so metimes desirable to have knowledge of the k shortest paths in contrast to simply a shortest path_ For example, the knowledge of good alternative routes (as opposed to just the shortest one) can be used by transportation planne rs to model more realistically the Aow of vehi cular traffi c on a road ne twork. Or, as a second example, the routing of messages through a communi cation s network when some routes are temporarily obstructed can be based on th e best alternative routes which are available. Several algorithms have been traditionally employed in order to determine the k shortest paths between specified nodes of a ne twork (such paths may in fac t con tain repeated nodes). An excellent survey of these algorithms is provided by the review article of Dreyfu s [1] 1. More recently, several new methods for performing s uch calculation s have been proposed [2 , 4]. These methods are based on a fairly strong analogy which exists be tween the solution of ne twork path problems and traditional techniques for solving ordinary linear equations. On the basi s of preliminary theoretical and computational evidence, one of these (the Double-Sweep method) emerged [4] as a reasonably effective procedure for calculating k shortest paths between a given node and all other nodes in a network.2 The purpose of this report is to describe a particular implementation of the Double-Sweep method in FORTRAN V 3 and to present a body of computational results for a practically important class of networks (namely, those with a rectangular grid topology).","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1974-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131507339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 45

A sufficient condition for matrix stability 矩阵稳定性的充分条件

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-07-01 DOI: 10.6028/JRES.078B.015

Charles R. Johnson

引用次数: 4

Rational equivalence of unimodular circulants 单模循环的有理等价

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-04-01 DOI: 10.6028/JRES.078B.008

S. Pierce

{"title":"Rational equivalence of unimodular circulants","authors":"S. Pierce","doi":"10.6028/JRES.078B.008","DOIUrl":"https://doi.org/10.6028/JRES.078B.008","url":null,"abstract":"Let P be the n X n matrix satisfying P I2= . . ,= P\" _ I , I/ = P \" , 1= 1 a nd all other entries O. The elements of the group rin g Z [P] are caJl ed integral circ ulants. Let G be the group in Z [P] consisting of the pos itive de finite symme tric unimodula r ele ments. M. Ne wma n [2, p. 198] as ks whi ch me mbers of G are ra tionall y equivalent to [ 1/. Th e a nswer to thi s question is in fact a n easy co nseque nce of th e Hasse norm theore m [1 , p. 186]. , TH EO REM : A LL members of G a re rat iona LLy equivalent to In. PROOF: Let A EG. As noted in [2 , p. 198] , we must show that an y eigenvalue A of A is of the form aa for some a in QI/' the nth cyclotomic fi e ld . Le t K be the real s ubfield of index 2 in Q\". We must show A is a norm from Q\" to K. If n = 2p \", p a prime, the n p is fully r amifi ed in Q 1/. I n any othe r case, Q\" is unramified over K at all finit e primes. So at most one finite prim e ramifies fro m K to Q\". N ow A is totally positive, so A is a norm at all Archimedean localiza tions. And A is a unit ; thu s A is a norm at all finite localizations, except , poss ibly, one. By the product formula , A is a norm ever ywhe re, and hence, by th e Hasse norm theore m, A is a global norm .","PeriodicalId":166823,"journal":{"name":"Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1974-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115487431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

How to determine accuracy of the output of a matrix inversion program 如何确定矩阵反演程序输出的精度

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-04-01 DOI: 10.6028/JRES.078B.009

M. Newman

引用次数: 5

Fixed-point solution of plant input/location problems 工厂输入/选址问题的定点解决方案

Journal of Research of the National Bureau of Standards, Section B: Mathematical Sciences Pub Date : 1974-04-01 DOI: 10.6028/JRES.078B.013

A. Goldman

引用次数: 2