Matches in SemOpenAlex for { <https://semopenalex.org/work/W2236698115> ?p ?o ?g. }
Showing items 1 to 74 of
74
with 100 items per page.
- W2236698115 abstract "This paper has been motivated by the curiosity that the circulant matrix ${rm Circ }(1/2, -1/4, 0, dots, 0,-1/4)$ is the $ntimes n$ positive semidefinite, tridiagonal matrix $A$ of smallest Euclidean norm having the property that $Ae = 0$ and $Af = f$, where $e$ and $f$ are, respectively, the vector of all $1$s and the vector of alternating $1$ and $-1$s. It then raises the following question (minimization problem): What should be the matrix $A$ if the tridiagonal restriction is replaced by a general bandwidth $2r + 1$ ($1leq r leq tfrac{n}{2 } -1$)? It is first easily shown that the solution of this problem must still be a circulant matrix. Then the determination of the first row of this circulant matrix consists in solving a least-squares problem having $tfrac{n}{2} , - 1$ nonnegative variables (Nonnegative Orthant) subject to $tfrac{n}{2} - r$ linear equations. Alternatively, this problem can be viewed as the minimization of the norm of an even function vanishing at the points $|i|>r$ of the set $left{-tfrac{n}{2} + 1, dots, -1, 0, 1, dots ,tfrac{n}{2} right}$, and whose Fourier-transform is nonnegative, vanishes at zero, and assumes the value one at $tfrac{n}{2}$. Explicit solutions are given for the special cases of $r=tfrac{n}{2}$, $r=tfrac{n}{2} -1$, and $r=2$. The solution for the particular case of $r=2$ can be physically interpreted as the vibrational mode of a ring-like chain of masses and springs in which the springs link both the nearest neighbors (with positive stiffness) and the next-nearest neighbors (with negative stiffness). The paper ends wiih a numerical illustration of the six cases ($1leq r leq 6$)corresponding to $n=12$." @default.
- W2236698115 created "2016-06-24" @default.
- W2236698115 creator A5086759859 @default.
- W2236698115 date "2015-02-08" @default.
- W2236698115 modified "2023-09-27" @default.
- W2236698115 title "Matrices of minimum norm satisfying certain prescribed band and spectral restrictions -- an extremal characterization of the discrete periodic Laplacian" @default.
- W2236698115 cites W1536329667 @default.
- W2236698115 cites W2039557338 @default.
- W2236698115 cites W2047605837 @default.
- W2236698115 cites W2050958540 @default.
- W2236698115 cites W2067100748 @default.
- W2236698115 cites W2091560152 @default.
- W2236698115 cites W2168127926 @default.
- W2236698115 doi "https://doi.org/10.13001/1081-3810.3068" @default.
- W2236698115 hasPublicationYear "2015" @default.
- W2236698115 type Work @default.
- W2236698115 sameAs 2236698115 @default.
- W2236698115 citedByCount "1" @default.
- W2236698115 countsByYear W22366981152021 @default.
- W2236698115 crossrefType "journal-article" @default.
- W2236698115 hasAuthorship W2236698115A5086759859 @default.
- W2236698115 hasConcept C106487976 @default.
- W2236698115 hasConcept C114614502 @default.
- W2236698115 hasConcept C115973184 @default.
- W2236698115 hasConcept C121332964 @default.
- W2236698115 hasConcept C158693339 @default.
- W2236698115 hasConcept C159985019 @default.
- W2236698115 hasConcept C17744445 @default.
- W2236698115 hasConcept C191795146 @default.
- W2236698115 hasConcept C192562407 @default.
- W2236698115 hasConcept C199539241 @default.
- W2236698115 hasConcept C33923547 @default.
- W2236698115 hasConcept C51647924 @default.
- W2236698115 hasConcept C62520636 @default.
- W2236698115 hasConceptScore W2236698115C106487976 @default.
- W2236698115 hasConceptScore W2236698115C114614502 @default.
- W2236698115 hasConceptScore W2236698115C115973184 @default.
- W2236698115 hasConceptScore W2236698115C121332964 @default.
- W2236698115 hasConceptScore W2236698115C158693339 @default.
- W2236698115 hasConceptScore W2236698115C159985019 @default.
- W2236698115 hasConceptScore W2236698115C17744445 @default.
- W2236698115 hasConceptScore W2236698115C191795146 @default.
- W2236698115 hasConceptScore W2236698115C192562407 @default.
- W2236698115 hasConceptScore W2236698115C199539241 @default.
- W2236698115 hasConceptScore W2236698115C33923547 @default.
- W2236698115 hasConceptScore W2236698115C51647924 @default.
- W2236698115 hasConceptScore W2236698115C62520636 @default.
- W2236698115 hasLocation W22366981151 @default.
- W2236698115 hasOpenAccess W2236698115 @default.
- W2236698115 hasPrimaryLocation W22366981151 @default.
- W2236698115 hasRelatedWork W127006096 @default.
- W2236698115 hasRelatedWork W1536823598 @default.
- W2236698115 hasRelatedWork W1544518263 @default.
- W2236698115 hasRelatedWork W1578537165 @default.
- W2236698115 hasRelatedWork W1596352804 @default.
- W2236698115 hasRelatedWork W2004556758 @default.
- W2236698115 hasRelatedWork W2024336882 @default.
- W2236698115 hasRelatedWork W2042111418 @default.
- W2236698115 hasRelatedWork W2046040002 @default.
- W2236698115 hasRelatedWork W2071109732 @default.
- W2236698115 hasRelatedWork W2076990273 @default.
- W2236698115 hasRelatedWork W2154864636 @default.
- W2236698115 hasRelatedWork W2253470506 @default.
- W2236698115 hasRelatedWork W2386168744 @default.
- W2236698115 hasRelatedWork W2403620909 @default.
- W2236698115 hasRelatedWork W2547037564 @default.
- W2236698115 hasRelatedWork W2775907061 @default.
- W2236698115 hasRelatedWork W2951302857 @default.
- W2236698115 hasRelatedWork W2964349534 @default.
- W2236698115 hasRelatedWork W77245334 @default.
- W2236698115 isParatext "false" @default.
- W2236698115 isRetracted "false" @default.
- W2236698115 magId "2236698115" @default.
- W2236698115 workType "article" @default.