TY - JOUR
TI - Isometries on L^p Spaces and Copies of L^p shifts
AU - Campbell, Stephen L.
AU - Faulkner, G.D.
AU - Gardner, M.L.
T2 - Proceedings of the American Mathematical Society
DA - 1979/11//
PY - 1979/11//
DO - 10.2307/2042638
VL - 77
IS - 2
SP - 198–200
SN - 0002-9939 1088-6826
ER -
TY - JOUR
TI - The stable solutions of quadratic matrix equations
AU - Campbell, Stephen L.
AU - Daughtry, John
T2 - Proceedings of the American Mathematical Society
DA - 1979///
PY - 1979///
VL - 74
IS - 1
SP - 19–23
ER -
TY - CONF
TI - A functional analytic approach to autonomous linear singular perturbation problems
AU - Campbell, Stephen L.
T2 - Annual Allerton Conference on Communication, Control, and Computing
C2 - 1979///
C3 - Proceedings of the Seventeenth Annual Allerton Conference on Communication, Control, and Computing
DA - 1979///
PY - 1979///
SP - 445–463
ER -
TY - CHAP
TI - Isometries, projections and Wold decompositions
AU - Campbell, Stephen L.
AU - Faulkner, G.D.
AU - Sine, Robert
T2 - Operator Theory and Functional Analysis
A2 - Erdelyi, Ivan
T3 - Research notes in mathematics
PY - 1979///
SP - 84–114
PB - Pitman Publishing Company
SN - 9780822484509 9780273084501
SV - 38
ER -
TY - JOUR
TI - On the Randomness of Eigenvectors Generated from Networks with Random Topologies
AU - Silverstein, Jack W.
T2 - SIAM Journal on Applied Mathematics
AB - A model for the generation of neural connections at birth led to the study of W, a random, symmetric, nonnegative definite linear operator defined on a finite, but very large, dimensional Euclidean space [1]. A limit law, as the dimension increases, on the eigenvalue spectrum of W was proven, implying that realizations of W (being identified with organisms in a species) appear totally different on the microscopic level and yet have almost identical spectral densities. The present paper considers the eigenvectors of W. Evidence is given to support the conjecture that, contrary to the deterministic aspect of the eigenvalues, the eigenvectors behave in a completely chaotic manner, which is described in terms of the normalized uniform (Haar) measure on the group of orthogonal transformations on a finite dimensional space. The validity of the conjecture would imply a tabula rasa property on the ensemble (“species”) of all realizations of W.
DA - 1979/10//
PY - 1979/10//
DO - 10.1137/0137014
VL - 37
IS - 2
SP - 235-245
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/0137014
DB - Crossref
ER -
TY - JOUR
TI - On a singularly perturbed autonomous linear control problem
AU - Campbell, S.
T2 - IEEE Transactions on Automatic Control
AB - A singularly perturbed autonomous control process is examined. The relationship between the original and the reduced problem is developed.
DA - 1979/2//
PY - 1979/2//
DO - 10.1109/tac.1979.1101951
VL - 24
IS - 1
SP - 115-117
J2 - IEEE Trans. Automat. Contr.
LA - en
OP -
SN - 0018-9286
UR - http://dx.doi.org/10.1109/tac.1979.1101951
DB - Crossref
ER -
TY - JOUR
TI - Singular Perturbation of Autonomous Linear Systems
AU - Campbell, Stephen L.
AU - Rose, Nicholas J.
T2 - SIAM Journal on Mathematical Analysis
AB - Let $X_\varepsilon (t) = \exp (({{A + B} /\varepsilon })t)$ where A, B are $n \times n$ matrices. It is shown that $X_\varepsilon (t)$ converges pointwise for $t > 0$ as $\varepsilon \to 0^ + $ if and only if Index $B \leqq 1$ and the nonzero eigenvalues of B have negative real part. An explicit representation of the limit of $X_\varepsilon (t)$ is given. These results are applied to the singularly perturbed system $\dot x = A_1 (\varepsilon )x + A_2 (\varepsilon )y$, $\varepsilon \dot y = B_1 (\varepsilon )x + B_2 (\varepsilon )y$. This paper differs from earlier work both in the derivation of necessary and sufficient conditions and in the explicit forms for the limits.
DA - 1979/5//
PY - 1979/5//
DO - 10.1137/0510051
VL - 10
IS - 3
SP - 542-551
J2 - SIAM J. Math. Anal.
LA - en
OP -
SN - 0036-1410 1095-7154
UR - http://dx.doi.org/10.1137/0510051
DB - Crossref
ER -
TY - JOUR
TI - Limit behavior of solutions of singular difference equations
AU - Campbell, Stephen L.
T2 - Linear Algebra and its Applications
AB - Necessary and sufficient conditions for a solution {zk} of the difference equation Azk+1+Bzk = b, k ⩾0, with A singular, to be a convergent sequence of vectors are given under a variety of assumptions. Theoretical results on iterative schemes for solving Ax = b by singular splittings, A = A+B, are given first. In particular, the case when A = A∗ and A is positive semi-definite is considered. Then applications to discrete control problems and backwards population projection are discussed.
DA - 1979/2//
PY - 1979/2//
DO - 10.1016/0024-3795(79)90100-9
VL - 23
SP - 167-178
J2 - Linear Algebra and its Applications
LA - en
OP -
SN - 0024-3795
UR - http://dx.doi.org/10.1016/0024-3795(79)90100-9
DB - Crossref
ER -
TY - JOUR
TI - Solution of H-Equations by Iteration
AU - Kelley, C. T.
T2 - SIAM Journal on Mathematical Analysis
AB - Previous article Next article Solution of H-Equations by IterationC. T. KelleyC. T. Kelleyhttps://doi.org/10.1137/0510080PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractA generalization of the Chandrasekhar H-equation is solved by iteration. Such equations are of interest in heat transfer.[1] R. L. Bowden and , P. F. Zweifel, A Banach space analysis of the Chandrasekhar H-equation, Astrophys. J., 210 (1976), 178–183 10.1086/154816 MR0438981 (55:11883) CrossrefISIGoogle Scholar[2] C. E. Siewert and , E. E. Burniston, Half-space analysis basic to the time dependent BGK model in the kinetic theory of gases, J. Mathematical Phys., 18 (1977), 376–380 10.1063/1.523279 MR0434272 (55:7240) CrossrefISIGoogle Scholar[3] S. Chandrasekhar, Radiative transfer, Dover Publications Inc., New York, 1960xiv+393 MR0111583 (22:2446) Google Scholar[4] J. T. Kriese, , T. S. Chang and , C. E. Siewert, Elementary solutions of coupled model equations in the kinetic theory of gases, Internat. J. Engrg. Sci., 12 (1974), 441–470 10.1016/0020-7225(74)90064-0 MR0459448 (56:17640) 0283.45017 CrossrefISIGoogle Scholar[5] A. L. Crosbie and , T. R. sawheny, Application of Ambarzumian's method to radiant interchange in a rectangular cavity, J. Heat Transfer, C96 (1974), 191–196 CrossrefISIGoogle Scholar[6] A. L. Crosbie and , T. R. sawheny, Radiant interchange in a nonisothermal rectangular cavity, AIAA J., 13 (1975), 425–431 0314.76067 CrossrefGoogle Scholar[7] C. T. Kelley and , T. W. Mullikin, Solution by iteration of H-equations in multigroup neutron transport, J. Mathematical Phys., 19 (1978), 500–501 10.1063/1.523673 MR0462389 (57:2363) 0382.45005 CrossrefISIGoogle Scholar[8] M. G. Krien, Integral equations on a half-line with kernel depending upon the difference of the arguments, Amer. Math. Soc. Transl., 22 (1962), 163–288 Google Scholar[9] L. B. Rall, Quadratic equations in Banach spaces, Rend. Circ. Mat. Palermo (2), 10 (1961), 314–332 MR0144184 (26:1731) 0193.43902 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Convergence of the EDIIS Algorithm for Nonlinear EquationsXiaojun Chen and C. T. Kelley17 January 2019 | SIAM Journal on Scientific Computing, Vol. 41, No. 1AbstractPDF (427 KB)A solution method for the linear Chandrasekhar equation1 January 2006 | Mathematical Methods in the Applied Sciences, Vol. 29, No. 15 Cross Ref Legendre spectral method for solving integral and integro-differential equationsInternational Journal of Computer Mathematics, Vol. 75, No. 2 Cross Ref A Fast Multilevel Algorithm for Integral EquationsC. T. Kelley14 July 2006 | SIAM Journal on Numerical Analysis, Vol. 32, No. 2AbstractPDF (1410 KB)Solution of the Chandrasekhar H ‐equation by Newton’s MethodJournal of Mathematical Physics, Vol. 21, No. 7 Cross Ref Volume 10, Issue 4| 1979SIAM Journal on Mathematical Analysis History Submitted:30 December 1977Published online:03 August 2006 InformationCopyright © 1979 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0510080Article page range:pp. 844-849ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics
DA - 1979/7//
PY - 1979/7//
DO - 10.1137/0510080
VL - 10
IS - 4
SP - 844-849
SN - 0036-1410 1095-7154
UR - http://dx.doi.org/10.1137/0510080
ER -
TY - JOUR
TI - Operator-valued Chandrasekhar H-functions
AU - Kelley, C.T.
T2 - Journal of Mathematical Analysis and Applications
DA - 1979///
PY - 1979///
VL - 70
SP - 579–588
ER -
TY - JOUR
TI - A variational equivalent to diagonal scaling
AU - Berger, Marc A
AU - Kelley, C.T
T2 - Journal of Mathematical Analysis and Applications
AB - This paper is concerned with the problem of diagonally scaling a given nonnegative matrix a to one with prescribed row and column sums. The approach is to represent one of the two scaling matrices as the solution of a variational problem. This leads in a natural way to necessary and sufficient conditions on the zero pattern of a so that such a scaling exists. In addition the convergence of the successive prescribed row and column sum normalizations is established. Certain invariants under diagonal scaling are used to actually compute the desired scaled matrix, and examples are provided. Finally, at the end of the paper, a discussion of infinite systems is presented.
DA - 1979/11//
PY - 1979/11//
DO - 10.1016/0022-247x(79)90290-7
VL - 72
IS - 1
SP - 291-304
J2 - Journal of Mathematical Analysis and Applications
LA - en
OP -
SN - 0022-247X
UR - http://dx.doi.org/10.1016/0022-247x(79)90290-7
DB - Crossref
ER -
TY - JOUR
TI - Nonregular Singular Dynamic Leontief Systems
AU - Campbell, Stephen L.
T2 - Econometrica
DA - 1979/11//
PY - 1979/11//
DO - 10.2307/1914020
VL - 47
IS - 6
SP - 1565
J2 - Econometrica
OP -
SN - 0012-9682
UR - http://dx.doi.org/10.2307/1914020
DB - Crossref
ER -