Kronecker Product Extensions of Linear Operators

Previous article Next article Kronecker Product Extensions of Linear OperatorsFrank StengerFrank Stengerhttps://doi.org/10.1137/0705033PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Marvin Marcus and , Henryk Minc, A survey of matrix theory and matrix inequalities, Allyn and Bacon Inc., Boston, Mass., 1964xvi+180 MR0162808 (29:112) 0126.02404 Google Scholar[2] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963xiv+393 MR0157156 (28:393) 0111.06003 Google Scholar[3] Henry C. Thacher, Jr., Generalization of concepts related to linear dependence, J. Soc. Indust. Appl. Math., 6 (1958), 288–299 10.1137/0106020 MR0095577 (20:2079) 0085.01303 LinkISIGoogle Scholar[4] B. Mond and , O. Shisha, On the approximation of functions of several variables, J. Res. Nat. Bur. Standards Sect. B, 70B (1966), 211–218 MR0217489 (36:578) 0161.25301 CrossrefGoogle Scholar[5] Frank Stenger, Error bounds for the evaluation of integrals by repeated Gauss-type formulae, Numer. Math., 9 (1966), 200–213 10.1007/BF02162084 MR0205462 (34:5289) 0147.35804 CrossrefISIGoogle Scholar[6] W. M. Kincaid, Note on the error in interpolation of a function of two independent variables, Ann. Math. Statistics, 19 (1948), 85–88 MR0024231 (9,470i) 0041.24304 CrossrefISIGoogle Scholar[7] Henry C. Thacher, Jr., Derivation of interpolation formulas in several independent variables, Ann. New York Acad. Sci., 86 (1960), 758–775 (1960) MR0116456 (22:7243) 0156.17302 ISIGoogle Scholar[8] Arthur Sard, Linear approximation, American Mathematical Society, Providence, R.I., 1963xi+544 MR0158203 (28:1429) 0115.05403 CrossrefGoogle Scholar[9] Richard von Mises, Numerische Berechnung mehrdimensionaler Integrale, Z. Angew. Math. Mech., 34 (1954), 201–210 MR0063777 (16,178d) 0056.28501 CrossrefGoogle Scholar[10] J. Meinguet, Methods for estimating the remainder in linear rules of approximation. Application to the Romberg algorithm, Numer. Math., 8 (1966), 345–366 10.1007/BF02162979 MR0199962 (33:8102) 0161.12704 CrossrefISIGoogle Scholar[11] J. N. Lyness and , C. B. Moler, Van der Monde systems and numerical differentiation, Numer. Math., 8 (1966), 458–464 MR0201071 (34:956) 0141.33404 CrossrefISIGoogle Scholar[12] Philip J. Davis and , Philip Rabinowitz, Numerical integration, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967ix+230 MR0211604 (35:2482) 0154.17802 Google Scholar[13] A. H. Stroud and , Don Secrest, Gaussian quadrature formulas, Prentice-Hall Inc., Englewood Cliffs, N.J., 1966ix+374 MR0202312 (34:2185) 0156.17002 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Sinc Methods on PolyhedraNew Sinc Methods of Numerical Analysis | 7 August 2020 Cross Ref The ubiquitous Kronecker productJournal of Computational and Applied Mathematics, Vol. 123, No. 1-2 | 1 Nov 2000 Cross Ref Matrices of Sinc methodsJournal of Computational and Applied Mathematics, Vol. 86, No. 1 | 1 Nov 1997 Cross Ref On the solvability of bivariate Hermite-Birkhoff interpolation problemsJournal of Computational and Applied Mathematics, Vol. 32, No. 1-2 | 1 Nov 1990 Cross Ref Reconstruction of two-dimensional signals from level crossingsProceedings of the IEEE, Vol. 78, No. 1 | 1 Jan 1990 Cross Ref Fully Symmetric Interpolatory Rules for Multiple IntegralsAlan GenzSIAM Journal on Numerical Analysis, Vol. 23, No. 6 | 14 July 2006AbstractPDF (1168 KB)An Extension of the Alternating Direction Galerkin Method to More General GeometriesH. I. El-Zorkany and R. BalasubramanianSIAM Journal on Numerical Analysis, Vol. 20, No. 2 | 17 July 2006AbstractPDF (1440 KB)Interpolatory inner product quadrature formulasBIT, Vol. 20, No. 4 | 1 Dec 1980 Cross Ref An algorithm for the electromagnetic scattering due to an axially symmetric body with an impedance boundary conditionJournal of Mathematical Analysis and Applications, Vol. 78, No. 2 | 1 Dec 1980 Cross Ref A "sinc-Galerkin" method of solution of boundary value problemsMathematics of Computation, Vol. 33, No. 145 | 1 January 1979 Cross Ref Numerical differentiation and the solution of multidimensional Vandermonde systemsMathematics of Computation, Vol. 24, No. 110 | 1 January 1970 Cross Ref Volume 5, Issue 2| 1968SIAM Journal on Numerical Analysis199-459 History Submitted:27 March 1967Published online:03 August 2006 InformationCopyright © 1968 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0705033Article page range:pp. 422-435ISSN (print):0036-1429ISSN (online):1095-7170Publisher:Society for Industrial and Applied Mathematics