Applications of Linear Programming to Numerical Analysis
1968; Society for Industrial and Applied Mathematics; Volume: 10; Issue: 2 Linguagem: Inglês
10.1137/1010029
ISSN1095-7200
Autores Tópico(s)Matrix Theory and Algorithms
ResumoNext article Applications of Linear Programming to Numerical AnalysisPhilip RabinowitzPhilip Rabinowitzhttps://doi.org/10.1137/1010029PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. Barrodale, Masters Thesis, Approximation in the L1 and L∞ norms by linear programming, Doctoral thesis, Dept. of Computational and Statistical Science, University of Liverpool, 1967 Google Scholar[2] I. Barrodale and , F. D. K. Roberts, An improved algorithm for discrete $l\sb{1}$ linear approximation, SIAM J. Numer. Anal., 10 (1973), 839–848 10.1137/0710069 MR0339449 0266.65016 LinkISIGoogle Scholar[3] I. Barrodale, An improved algorithm for discrete L∞ linear approximations, submitted Google Scholar[4] Ian Barrodale and , Andrew Young, Algorithms for best $L\sb{1}$ and $L\sb{\infty }$ linear approximations on a discrete set, Numer. Math., 8 (1966), 295–306 10.1007/BF02162565 MR0196912 0173.18801 CrossrefISIGoogle Scholar[5] Ian Barrodale and , Andrew Young, A note on numerical procedures for approximation by spline functions, Comput. J., 9 (1966), 318–320 MR0202278 0168.14905 CrossrefISIGoogle Scholar[6] I. Barrodale and , A. Young, Computational experience in solving linear operator equations using the Chebyshev norm, 1967, Numerical Approximation to Functions and Data, Proc. I. M. A. Conference held at University of Kent, Canterbury, to appear Google Scholar[7] R. E. Bellman, , H. H. Kagiwada and , R. B. Kalaba, Quasilinearization, boundary-value problems and linear programming, RM-4284-PR, The RAND Corporation, Santa Monica, California, 1964 Google Scholar[8] S. A. Berger and , W. C. Webster, R. L. Graves and , P. Wolfe, An application of linear programming to the fairing of ships' linesRecent Advances in Mathematical Programming, McGraw-Hill, New York, 1963, 241–253 Google Scholar[9] G. Bertram, Beziehungen zwischen Defektabschätzungen und "Linear programming" bei linearen Gleichungssystemen, Z. Angew. Math. Mech., 40 (1960), 373– MR0112245 0094.11003 CrossrefGoogle Scholar[10] L. Bittner, Das Austauschverfahren der linearen Tschebyscheff-Approximation bei nicht erfüllter Haarscher Bedingung, Z. Angew. Math. Mech., 41 (1961), 238–256 MR0175289 0103.28501 CrossrefGoogle Scholar[11] K. T. Boyd, Simultaneous equations and linear programming, Comput. J., 3 (1960/1961), 45–46, 50 10.1093/comjnl/3.1.45 MR0111126 0099.33105 CrossrefGoogle Scholar[12] J. H. Cannon, Masters Thesis, Backward continuation in time by numerical means of the solution of the heat equation in a rectangle, M. A. thesis, Rice University, Houston, Texas, 1960 Google Scholar[13] J. H. Cannon, Numerical continuation backwards in time for solutions of the heat equation and numerical continuation of solutions of Laplace's equation in a half space, Rep., 8135, Brookhaven National Laboratory, Upton, Long Island, New York Google Scholar[14] J. R. Cannon, The numerical solution of the Dirichlet problem for Laplace's equation by linear programming, J. Soc. Indust. Appl. Math., 12 (1964), 233–237 10.1137/0112022 MR0164453 0221.65186 LinkISIGoogle Scholar[15] J. R. Cannon, Error estimates for some unstable continuation problems, J. Soc. Indust. Appl. Math., 12 (1964), 270–284 10.1137/0112025 MR0168897 0134.08501 LinkISIGoogle Scholar[16] J. R. Cannon, D. Greenspan, Some numerical results for the solution of the heat equation backwards in timeNumerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966), John Wiley & Sons Inc., New York, 1966, 21–54 MR0207221 0196.50503 Google Scholar[17] J. R. Cannon and , Maria M. Cecchi, The numerical solution of some biharmonic problems by mathematical programming techniques, SIAM J. Numer. Anal., 3 (1966), 451–466 10.1137/0703039 MR0226877 0255.65038 LinkGoogle Scholar[18] J. R. Cannon and , Maria M. Cecchi, Numerical experiments on the solution of some biharmonic problems by mathematical programming techniques, SIAM J. Numer. Anal., 4 (1967), 147–154 10.1137/0704014 MR0213053 0255.65039 LinkGoogle Scholar[19] J. R. Cannon and , Jim Douglas, Jr., The Cauchy problem for the heat equation, SIAM J. Numer. Anal., 4 (1967), 317–336 10.1137/0704028 MR0216785 0154.36502 LinkGoogle Scholar[20] 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 0214.14805 LinkGoogle Scholar[21] A. Charnes and , W. W. Cooper, Management models and industrial applications of linear programming, John Wiley & Sons Inc., New York, 1961xxiii+pp. 1–467+4 MR0157773 0107.37004 Google Scholar[22] A. Charnes and , W. W. Cooper, R. E. Machol, , W. P. Tanner and , S. N. Alexander, Elements of a strategy for making models in linear programmingSystem Engineering Handbook, McGraw-Hill, New York, 1965, Chap. 26 Google Scholar[23] E. W. Cheney and , T. H. Southard, A survey of methods for rational approximation, with particular reference to a new method based on a forumla of Darboux, SIAM Rev., 5 (1963), 219–231 10.1137/1005065 MR0158531 LinkISIGoogle Scholar[24] L. Collatz, Methods for the solution of partial differential equations on digital computersInformation processing, UNESCO, Paris, 1960, 72–78 MR0148236 0115.34101 Google Scholar[25] Lothar Collatz, R. E. Langer, Approximation in partial differential equations, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, 413–422 MR0103593 0085.11201 Google Scholar[26] Lothar Collatz, The numerical treatment of differential equations. 3d ed, Translated from a supplemented version of the 2d German edition by P. G. Williams. Die Grundlehren der mathematischen Wissenschaften, Bd. 60, Springer-Verlag, Berlin, 1960xv+568 pp. (1 plate) MR0109436 0086.32601 CrossrefGoogle Scholar[27] L. Collatz, Tschebyscheffsche Approximation. Randwertaufgaben und Optimierungsaufgaben, Wiss. Z. Hochsch. Architektur Bauwesen Weimar, 12 (1965), 504–509 MR0202279 Google Scholar[28] Lothar Collatz, Functional analysis and numerical mathematics, Translated from the German by Hansjörg Oser, Academic Press, New York, 1966xx+473 MR0205126 0148.39002 Google Scholar[29] Lothar Collatz and , Wolfgang Wetterling, Optimierungsaufgaben, Heidelberger Taschenbücher, Band 15, Springer-Verlag, Berlin, 1966ix+181 MR0204157 0142.16602 CrossrefGoogle Scholar[30] Germund Dahlquist, , Sven-A˙ke Gustafson and , Károly Siklósi, Convergence acceleration from the point of view of linear programming, Nordisk Tidskr. Informations-Behandling, 5 (1965), 1–16 MR0181088 0146.14202 Google Scholar[31] George B. Dantzig, Linear programming and extensions, Princeton University Press, Princeton, N.J., 1963xvi+625 MR0201189 0108.33103 CrossrefGoogle Scholar[32] Philip J. Davis, A construction of nonnegative approximate quadratures, Math. Comp., 21 (1967), 578–582 MR0222534 0189.16401 CrossrefISIGoogle Scholar[33] Philip Davis and , Philip Rabinowitz, A multiple purpose orthonormalizing code and its uses, J. Assoc. Comput. Mach., 1 (1954), 183–191 MR0067578 CrossrefISIGoogle Scholar[34] Philip J. Davis and , Philip Rabinowitz, F. L. Alt, Advances in orthonormalizing computationAdvances in Computers, Vol. 2, Academic Press, New York, 1961, 55–133 MR0138189 0136.13405 CrossrefGoogle Scholar[35] J. Descloux, Masters Thesis, Contribution au calcul des approximations de Tschebicheff, Doctoral thesis, Ecole Polytechnique de Zurich, Lausanne, 1961 Google Scholar[36] M. L. Deutsch, Letter, Comm. ACM, 2 (1959), 1– CrossrefISIGoogle Scholar[37] Jim Douglas, Jr., R. E. Langer, A numerical method for analytic continuation, Boundary problems in differential equations, Univ. of Wisconsin Press, Madison, 1960, 179–189 MR0117866 0100.12405 Google Scholar[38] Jim Douglas, Jr., Mathematical programming and integral equationsSympos. on the Numerical Treatment of Ordinary Differential Equations, Integral and Integro-Differential Equations (Rome, 1960), Birkhäuser, Basel, 1960, 269–274 MR0164457 0108.29903 Google Scholar[39] Jim Douglas, Jr., J. H. Bramble, Approximate continuation of harmonic and parabolic functionsNumerical Solution of Partial Differential Equations (Proc. Sympos. Univ. Maryland, 1965), Academic Press, New York, 1966, 353–364 MR0202333 0161.12602 Google Scholar[40] R. J. Dufpin and , L. A. Karlovitz, Formulation of linear programs in analysis I: Approximation theory, Tech. Note, BN-486, University of Maryland, College Park, 1967 Google Scholar[41] Walter D. Fisher, A note on curve fitting with minimum deviations by linear programming., J. Amer. Statist. Assoc., 56 (1961), 359–362 MR0129115 0099.14302 CrossrefISIGoogle Scholar[42] P. Fox, , A. A. Goldstein and , G. Lastman, H. L. Garabedian, Rational approximations on finite point sets, Approximation of Functions (Proc. Sympos. General Motors Res. Lab., 1964), Elsevier Publ. Co., Amsterdam, 1965, 57–67 MR0190598 0263.65015 Google Scholar[43] D. R. Fulkerson and , P. Wolfe, An algorithm for scaling matrices, SIAM Rev., 4 (1962), 142–146 10.1137/1004032 MR0137587 0108.12401 LinkISIGoogle Scholar[44] Allen A. Goldstein and , Ward Cheney, A finite algorithm for the solution of consistent linear equations and inequalities and for the Tchebycheff approximation of inconsistent linear equations, Pacific J. Math., 8 (1958), 415–427 MR0101505 0084.01902 CrossrefGoogle Scholar[45] James E. Kelley, Jr., An application of linear programming to curve fitting, J. Soc. Indust. Appl. Math., 6 (1958), 15–22 10.1137/0106002 MR0092207 0084.15804 LinkISIGoogle Scholar[46] W. Krabs, Masters Thesis, Einige Methoden zur Lösung des diskreten linearen Tschebyscheff Problems, Dissertation, University of Hamburg, 1963 Google Scholar[47] L. V. Kantorovič, Some new approaches to computational methods and the handling of observations, Sibirsk. Mat. Ž., 3 (1962), 701–709 MR0189223 Google Scholar[48] H. L. Loeb, A note on rational function approximation, Convair Astronautics Applied Mathematics Series no. 27, San Diego, California, 1959 Google Scholar[49] Henry L. Loeb, Algorithms for Chebyshev approximations using the ratio of linear forms, J. Soc. Indust. Appl. Math., 8 (1960), 458–465 10.1137/0108031 MR0119383 0103.10602 LinkISIGoogle Scholar[50] O. L. Mangasarian, Numerical solution of the first biharmonic problem by linear programming, Internat. J. Engrg. Sci., 1 (1963), 231–240 10.1016/0020-7225(63)90035-1 MR0149684 0137.13904 CrossrefGoogle Scholar[51] 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 0145.14203 CrossrefISIGoogle Scholar[52] D. G. Moursund, Chebyshev approximations of a function and its derivatives, Math. Comp., 18 (1964), 382–389 MR0166529 0119.32903 CrossrefISIGoogle Scholar[53] D. G. Moursund, Some computational aspects of the uniform approximation of a function and its derivative, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), 464–472 MR0187373 0139.11203 LinkGoogle Scholar[54] W. Oettli, On the solution set of a linear system with inaccurate coefficients, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), 115–118 MR0178567 0146.13404 LinkGoogle Scholar[55] W. Oettli and , W. Prager, Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides, Numer. Math., 6 (1964), 405–409 10.1007/BF01386090 MR0168106 0133.08603 CrossrefGoogle Scholar[56] W. Oettli, , W. Prager and , J. H. Wilkinson, Admissible solutions of linear systems with not sharply defined coefficients, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 2 (1965), 291–299 MR0184416 0154.16903 LinkGoogle Scholar[57] A. Orden, A. Orden and , L. Goldstein, Application of the simplex method to a variety of matrix problems, Symposium on Linear Inequalities and Programming, 1952, 28–50, Project SCOOP, Manual no. 10 Google Scholar[58] M. R. Osborne and , G. A. Watson, On the best linear Chebyshev approximation, Comput. J., 10 (1967), 172–177 MR0218808 0155.48101 CrossrefISIGoogle Scholar[59] John R. Rice, The approximation of functions. Vol. I: Linear theory, Addison-Wesley Publishing Co., Reading, Mass.-London, 1964xi+203 MR0166520 0114.27001 Google Scholar[60] J. B. Rosen, Chebyshev solution of large linear systems, J. Comput. System Sci., 1 (1967), 29–43 MR0229376 0148.39102 CrossrefGoogle Scholar[61] J. B. Rosen, D. Greenspan, Approximate computational solution of non-linear parabolic partial differential equations by linear programmingNumerical Solutions of Nonlinear Differential Equations (Proc. Adv. Sympos., Madison, Wis., 1966), John Wiley & Sons Inc., New York, 1966, 265–296 MR0207232 0258.65111 Google Scholar[62] J. B. Rosen, Private communication Google Scholar[63] J. B. Rosser, Estimation of capacity with bounds for the error, I, Tech. Summary Rep., 645, Mathematics Research Center, University of Wisconsin, Madison, 1966 Google Scholar[64] A. Stajano, A method for solving large systems of linear equations, 1966, Z77-6133, IBM Technical Information Exchange Google Scholar[65] Eduard L. Stiefel, R. E. Langer, Numerical methods of Tchebycheff approximation, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, 217–232 MR0107961 0083.35502 Google Scholar[66] E. Stiefel, Note on Jordan elimination, linear programming and Tchebycheff approximation, Numer. Math., 2 (1960), 1–17 10.1007/BF01386203 MR0111124 0097.32306 CrossrefGoogle Scholar[67] E. Stiefel, Methods—old and new—for solving the Tchebycheff approximation problem, J. Soc. Indust. Appl. Math. Ser. B Numer. Anal., 1 (1964), 164–176 MR0177501 0141.33502 LinkGoogle Scholar[68] S. Vajda, Mathematical programming, Addison-Wesley Series in Statistics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1961ix+310 MR0135621 0102.36401 Google Scholar[69] S. Vajda, J. Walsh, Techniques of operational researchNumerical Analysis, an Introduction, Thompson Book Co., Washington, D.C., 1967, 165–173 Google Scholar[70] Harvey M. Wagner, Linear programming techniques for regression analysis, J. Amer. Statist. Assoc., 54 (1959), 206–212 MR0130753 0088.35702 CrossrefISIGoogle Scholar[71] Harvey M. Wagner, Non-linear regression with minimal assumptions, J. Amer. Statist. Assoc., 57 (1962), 572–578 MR0146930 0139.36602 CrossrefISIGoogle Scholar[72] L. E. Ward, Jr., Classroom Notes: Linear Programming and Approximation Problems, Amer. Math. Monthly, 68 (1961), 46–53 MR1531057 CrossrefISIGoogle Scholar[73] W. Wetterling, Lösungsschranken beim Differenzenverfahren zur Potentialgleichung, Institut für Angewandte Mathematik der Universität, Hamburg, , 1966– Google Scholar[74] P. Wynn, Numerical efficiency profile functions, Nederl. Akad. Wetensch. Proc. Ser. A 65 = Indag. Math., 24 (1962), 118–126 MR0139257 0105.10002 CrossrefGoogle Scholar[75] J. D. Young, Application of linear programming to the numerical solution of linear differential equations, UCRL-10110, Lawrence Radiation Laboratory, Berkeley, California, 1962 Google Scholar[76] Jonathan D. Young, Linear program approach to linear differential problems, Internat. J. Engrg. Sci., 2 (1964), 413–416 10.1016/0020-7225(64)90019-9 MR0169383 0134.13404 CrossrefGoogle Scholar[77] S. I. Zuhovickii and , R. A. Poljak, An algorithm for solving the problem of rational Chebyshev approximation, Soviet Math., 5 (1964), 1574–1577 0143.39003 Google Scholar Next article FiguresRelatedReferencesCited byDetails Using Parameter Elimination to Solve Discrete Linear Chebyshev Approximation Problems13 December 2020 | Mathematics, Vol. 8, No. 12 Cross Ref Functional Approximations Cross Ref Optimisation Cross Ref Barycentric-Remez algorithms for best polynomial approximation in the chebfun system10 October 2009 | BIT Numerical Mathematics, Vol. 49, No. 4 Cross Ref Least Absolute Deviation Estimation of Linear Econometric Models: A Literature ReviewSSRN Electronic Journal Cross Ref Approximation Schemes for Infinite Linear ProgramsOnésimo Hernández-Lerma and Jean B. 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