Stabilized Numerical Analytic Prolongation with Poles

Abstract

Previous article Next article Stabilized Numerical Analytic Prolongation with PolesKeith MillerKeith Millerhttps://doi.org/10.1137/0118029PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] George A. Baker, Jr., The theory and application of the Padé approximant methodAdvances in Theoretical Physics, Vol. 1, Academic Press, New York, 1965, 1–58 MR0187807 (32:5253) Google Scholar[2] M. Bertero and , G. A. Viano, On the numerical analytic continuation of the proton electromagnetic form factors, Nuovo Cimento (10), 38 (1965), 1915–1920 MR0195458 (33:3658) CrossrefISIGoogle Scholar[3] J. R. Cannon and , Keith Miller, Some problems in numerical analytic continuation, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), 87–98 MR0179908 (31:4145) 0214.14805 LinkGoogle Scholar[4] G. F. Chew, S-Matrix Theory of Strong Interactions, W. A. Benjamin, New York, 1963 0138.45904 Google Scholar[5] Jim Douglas, Jr., A numerical method for analytic continuation, Boundary problems in differential equations, Univ. of Wisconsin Press, Madison, 1960, 179–189 MR0117866 (22:8640) 0100.12405 Google Scholar[6] A. Gorny, Contribution à l'étude des fonctions dérivables d'une variable réelle, Acta Math., 71 (1939), 317–358 MR0000848 (1,137d) 0022.15404 CrossrefGoogle Scholar[7] S. Ja. Havinson, The theory of extremal problems for bounded analytic functions satisfying additional conditions inside the domain, Uspehi Mat. Nauk, 18 (1963), 25–98 MR0150299 (27:300) 0149.03302 Google Scholar[8] Maurice H. Heins, On a problem of Walsh concerning the Hadamard three circles theorem, Trans. Amer. Math. Soc., 55 (1944), 349–372 MR0010190 (5,259b) 0060.21806 CrossrefGoogle Scholar[9] Keith Miller, Three circle theorems in partial differential equations and applications to improperly posed problems, Arch. Rational Mech. Anal., 16 (1964), 126–154 10.1007/BF00281335 MR0164136 (29:1435) 0145.14203 CrossrefISIGoogle Scholar[10] Keith Miller, An eigenfunction expansion method for problems with overspecified data, Ann. Scuola Norm. Sup. Pisa (3), 19 (1965), 397–405 MR0183972 (32:1448) 0145.14301 Google Scholar[11] Keith Miller, Least squares methods for ill-posed problems with a prescribed bound., SIAM J. Math. Anal., 1 (1970), 52–74 10.1137/0501006 MR0260196 (41:4824) 0214.14804 LinkGoogle Scholar[12] K. Miller, On finding bounds from monotone implicit inequalities, to appear Google Scholar[13] T. Regge, Introduction to complex orbital momenta, Nuovo Cimento (10), 14 (1959), 951–976 MR0143532 (26:1088) 0087.42903 CrossrefISIGoogle Scholar[14] T. Regge, Bound states, shadow states and Mandelstam representation, Nuovo Cimento (10), 18 (1960), 947–956 MR0143533 (26:1089) CrossrefISIGoogle Scholar[15] T. Regge and , G. A. Viano, The interpolation problem in the theory of complex angular momentum., Nuovo Cimento (10), 25 (1962), 709–722 MR0144675 (26:2217) 0106.10905 CrossrefISIGoogle Scholar[16] L. Schlessinger and , C. Schwartz, Analyticity as a useful computational tool, Phys. Rev. Lett., 16 (1966), 1173– 10.1103/PhysRevLett.16.1173 CrossrefISIGoogle Scholar[17] L. Schlessinger, Masters Thesis, The use of analyticity in the calculation of non-relativistic scattering amplitudes, Doctoral thesis, Univ. of California, Berkeley, 1967 Google Scholar[18] C. Sshwartz, On the information content of the Born series, J. Comp. Phys., 1 (1966), 91– 0242.65011 Google Scholar[19] J. L. Walsh, Interpolation and Approximation, Colloquium Publications, Vol. XX, American Mathematical Society, New York, 1935 0013.05903 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Data-Driven Algorithms for Signal Processing with Trigonometric Rational FunctionsHeather Wilber, Anil Damle, and Alex Townsend24 May 2022 | SIAM Journal on Scientific Computing, Vol. 44, No. 3AbstractPDF (2097 KB)Quantifying the ill-conditioning of analytic continuation28 January 2020 | BIT Numerical Mathematics, Vol. 60, No. 4 Cross Ref Capturing Chemistry in Action with Electrons: Realization of Atomically Resolved Reaction Dynamics7 June 2017 | Chemical Reviews, Vol. 117, No. 16 Cross Ref Orthogonal polynomial approach to estimation of poles of rational functions from data on open curvesJournal of Computational and Applied Mathematics, Vol. 273 Cross Ref Analytic sensing for multi-layer spherical models with application to EEG source imagingInverse Problems & Imaging, Vol. 7, No. 4 Cross Ref Algebraic reconstruction of the general-order poles of a meromorphic function20 January 2012 | Inverse Problems, Vol. 28, No. 2 Cross Ref Direct localization of poles of a meromorphic function from measurements on an incomplete boundary17 December 2009 | Inverse Problems, Vol. 26, No. 1 Cross Ref On Complex-valued 2D Eikonals. Part Four: Continuation Past a Caustic5 November 2009 | Milan Journal of Mathematics, Vol. 77, No. 1 Cross Ref Analytic Sensing: Noniterative Retrieval of Point Sources from Boundary MeasurementsD. Kandaswamy, T. Blu, and D. Van De Ville31 July 2009 | SIAM Journal on Scientific Computing, Vol. 31, No. 4AbstractPDF (708 KB)Reconstruction of the number and positions of dipoles and quadrupoles using an algebraic method26 November 2008 | Journal of Physics: Conference Series, Vol. 135 Cross Ref An algebraic method for identification of dipoles and quadrupoles18 February 2008 | Inverse Problems, Vol. 24, No. 2 Cross Ref Inverting sampled trafficIEEE/ACM Transactions on Networking, Vol. 14, No. 1 Cross Ref Reconstruction of thin conductivity imperfections, II. The case of multiple segmentsApplicable Analysis, Vol. 85, No. 1-3 Cross Ref Inverse source problem in an anisotropic medium by boundary measurements15 August 2005 | Inverse Problems, Vol. 21, No. 5 Cross Ref Recovery of pointwise sources or small inclusions in 2D domains and rational approximation10 November 2004 | Inverse Problems, Vol. 21, No. 1 Cross Ref Identification of simple poles via boundary measurements and an application of EIT25 September 2004 | Inverse Problems, Vol. 20, No. 6 Cross Ref On the reconstruction of diffusions from first-exit time distributions22 May 2004 | Inverse Problems, Vol. 20, No. 4 Cross Ref A Review of Selected Works on Crack Identification Cross Ref Boundary integral formulae for the reconstruction of electric and electromagnetic inhomogeneities of small volume15 September 2003 | ESAIM: Control, Optimisation and Calculus of Variations, Vol. 9 Cross Ref Resonance expansions of scattered waves28 July 2000 | Communications on Pure and Applied Mathematics, Vol. 53, No. 10 Cross Ref Identification of conductivity imperfections of small diameter by boundary measurements. Continuous dependence and computational reconstruction1 January 1999 | Inverse Problems, Vol. 14, No. 3 Cross Ref Rational approximations of fluid propertiesFluid Phase Equilibria, Vol. 88 Cross Ref Locations and strengths of point sources: stability estimates1 January 1999 | Inverse Problems, Vol. 8, No. 6 Cross Ref Energy-dependent phase-shift analysis of H2+4 He scattering in the energy range 0.87< Ed <5.24 MeV1 February 1991 | Physical Review C, Vol. 43, No. 2 Cross Ref Identification of small inhomogeneities of extreme conductivity by boundary measurements: a theorem on continuous dependenceArchive for Rational Mechanics and Analysis, Vol. 105, No. 4 Cross Ref Padé approximant technique for processing scattering data I. Theory, models and parametrization of the scattering dataCzechoslovak Journal of Physics, Vol. 39, No. 6 Cross Ref The formation of a rational S matrix using phase shifts from elastic scatteringJournal of Computational Physics, Vol. 78, No. 2 Cross Ref Rational S matrices and NN interactions1 April 1985 | Physical Review C, Vol. 31, No. 4 Cross Ref Search for physical structures on the boundary by optimal analytic continuation from a finite set of interior data points1 April 1983 | Physical Review D, Vol. 27, No. 7 Cross Ref An asymmetric form of the discrete Schrodinger equation with application to the inverse tunnelling problem1 January 1999 | Journal of Physics A: Mathematical and General, Vol. 14, No. 9 Cross Ref Analytic extrapolation techniques and stability problems in dispersion relation theoryPhysics Reports, Vol. 17, No. 4 Cross Ref On the analytic extrapolation of scattering amplitudes in L2 normNuclear Physics B, Vol. 56, No. 1 Cross Ref Some general remarks on improperly posed problems for partial differential equations22 August 2006 Cross Ref On the stability of the complex angular-momentum continuationNuclear Physics B, Vol. 25, No. 2 Cross Ref Volume 18, Issue 2| 1970SIAM Journal on Applied Mathematics History Submitted:24 December 1968Published online:01 August 2006 InformationCopyright © 1970 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0118029Article page range:pp. 346-363ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics