Bulletin of the American Mathematical Society

MathSciNet review: 1566906
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Book Information:

Author: Erich Bohl
Title: Monotonie: Lösbarkeit und Numerik bei Operatorgleichungen
Additional book information: Springer Tracts in Natural Philosophy, vol. 25, Springer-Verlag, Berlin, Heidelberg, New York, 1974, ix + 255 pp., $26.20.

Author: Walter Mead Patterson 3rd
Title: Iterative methods for the solution of a linear operator equation in Hilbert space-A survey
Additional book information: Lecture Notes in Mathematics, vol. 394, Springer-Verlag, Berlin, Heidelberg, New York, 1974, 183 pp., $8.20.

1.

M. Altman, Approximation methods in functional analysis, Lecture note, California Institute of Technology, Pasadena, Calif., 1959.

Philip M. Anselone, Collectively compact operator approximation theory and applications to integral equations, Prentice-Hall Series in Automatic Computation, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. With an appendix by Joel Davis. MR 0443383

Jean-Pierre Aubin, Approximation of elliptic boundary-value problems, Pure and Applied Mathematics, Vol. XXVI, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1972. MR 0478662

Gabriel Stolzenberg, Review: Foundations of constructive analysis by Errett Bishop, Bull. Amer. Math. Soc. 76 (1970), 301–323. MR 257687, DOI 10.1090/S0002-9904-1970-12455-7

E. K. Blum, Numerical analysis and computation theory and practice, Addison-Wesley Series in Mathematics, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1972. MR 0408185

H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert, North-Holland Mathematics Studies, No. 5, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York, 1973 (French). MR 0348562

Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R.I., 1976, pp. 1–308. MR 0405188

Lothar Collatz, Funktionalanalysis und numerische Mathematik, Die Grundlehren der mathematischen Wissenschaften, Band 120, Springer-Verlag, Berlin, 1964 (German). MR 0165651

Jane Cronin, Fixed points and topological degree in nonlinear analysis, Mathematical Surveys, No. 11, American Mathematical Society, Providence, R.I., 1964. MR 0164101

James W. Daniel, The approximate minimization of functionals, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1971. MR 0272398

Vladimir F. Demyanov and Aleksandr M. Rubinov, Approximate methods in optimization problems, Modern Analytic and Computational Methods in Science and Mathematics, No. 32, American Elsevier Publishing Co., Inc., New York, 1970. Translated from the Russian by Scripta Technica, Inc; Translation edited by George M. Kranc. MR 0266018

Peter L. Falb and Jan L. de Jong, Some successive approximation methods in control and oscillation theory, Mathematics in Science and Engineering, Vol. 59, Academic Press, New York-London, 1969. MR 0264855

Allen A. Goldstein, Constructive real analysis, Harper & Row, Publishers, New York-London, 1967. MR 0217616

14.

L. V. Kantorovič, Functional analysis and applied mathematics, Uspehi Mat. Nauk 3 (1948), no. 6 (28), 89-185; English transl., Nat. Bur. Standards Rep., no. 1509, U. S. Dept. of Commerce, Nat. Bur. Standards, Washington, D. C., 1952. MR 10, 380; 14, 766. MR 27947

L. V. Kantorovič, Functional analysis and applied mathematics, Uspehi Matem. Nauk (N.S.) 3 (1948), no. 6(28), 89–185 (Russian). MR 0027947

L. V. Kantorovich and G. P. Akilov, Functional analysis in normed spaces, International Series of Monographs in Pure and Applied Mathematics, Vol. 46, The Macmillan Company, New York, 1964. Translated from the Russian by D. E. Brown; Edited by A. P. Robertson. MR 0213845

M. A. Krasnosel’skii, Topological methods in the theory of nonlinear integral equations, A Pergamon Press Book, The Macmillan Company, New York, 1964. Translated by A. H. Armstrong; translation edited by J. Burlak. MR 0159197

M. A. Krasnosel′skiĭ, Positive solutions of operator equations, P. Noordhoff Ltd., Groningen, 1964. Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron. MR 0181881

M. A. Krasnosel′skiĭ, G. M. Vaĭnikko, P. P. Zabreĭko, Ya. B. Rutitskii, and V. Ya. Stetsenko, Approximate solution of operator equations, Wolters-Noordhoff Publishing, Groningen, 1972. Translated from the Russian by D. Louvish. MR 0385655

N. S. Kurpel′, Proektsionno-iterativnye metody resheniya operatornykh uravneniĭ, Izdat. “Naukova Dumka”, Kiev, 1968 (Russian). MR 0254691

J. P. LaSalle and S. Lefschetz (eds.), Recent Soviet contributions to mathematics, The Macmillan Company, New York, 1962. MR 0167383

S. G. Mikhlin, The numerical performance of variational methods, Wolters-Noordhoff Publishing, Groningen, 1971. Translated from the Russian by R. S. Anderssen. MR 0278506

M. Z. Nashed, Differentiability and related properties of nonlinear operators: Some aspects of the role of differentials in nonlinear functional analysis, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1971, pp. 103–309. MR 0276840

M. Z. Nashed, Generalized inverses, normal solvability, and iteration for singular operator equations, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970) Academic Press, New York, 1971, pp. 311–359. MR 0275246

M. Zuhair Nashed (ed.), Generalized inverses and applications, University of Wisconsin, Mathematics Research Center, Publication No. 32, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0451661

Herman H. Goldstine and John von Neumann, Numerical inverting of matrices of high order. II, Proc. Amer. Math. Soc. 2 (1951), 188–202. MR 41539, DOI 10.1090/S0002-9939-1951-0041539-X

J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York-London, 1970. MR 0273810

A. M. Ostrowski, Solution of equations in Euclidean and Banach spaces, Pure and Applied Mathematics, Vol. 9, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1973. Third edition of Solution of equations and systems of equations. MR 0359306

W. V. Petryshyn, On the approximation-solvability of equations involving $A$-proper and psuedo-$A$-proper mappings, Bull. Amer. Math. Soc. 81 (1975), 223–312. MR 388173, DOI 10.1090/S0002-9904-1975-13728-1

Louis B. Rall, Computational solution of nonlinear operator equations, John Wiley & Sons, Inc., New York-London-Sydney, 1969. With an appendix by Ramon E. Moore. MR 0240944

Louis B. Rall (ed.), Nonlinear functional analysis and applications, Academic Press, New York-London, 1971. MR 0272576

Alexandru I. Şchiop, Metode aproximative în analiza neliniară, Editura Academiei Republicii Socialiste România, Bucharest, 1972 (Romanian). With an English summary. MR 0349008

J. T. Schwartz, Nonlinear functional analysis, Notes on Mathematics and its Applications, Gordon and Breach Science Publishers, New York-London-Paris, 1969. Notes by H. Fattorini, R. Nirenberg and H. Porta, with an additional chapter by Hermann Karcher. MR 0433481

Ivan Singer, Best approximation in normed linear spaces by elements of linear subspaces, Die Grundlehren der mathematischen Wissenschaften, Band 171, Publishing House of the Academy of the Socialist Republic of Romania, Bucharest; Springer-Verlag, New York-Berlin, 1970. Translated from the Romanian by Radu Georgescu. MR 0270044

M. M. Vainberg, Variational methods for the study of nonlinear operators, Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, 1964. With a chapter on Newton’s method by L. V. Kantorovich and G. P. Akilov. Translated and supplemented by Amiel Feinstein. MR 0176364

M. M. Vaĭnberg, Variatsionnyĭ metod i metod monotonnykh operatorov v teorii nelineĭnykh uravneniĭ, Izdat. “Nauka”, Moscow, 1972 (Russian). MR 0467427

M. M. Vaĭnberg and V. A. Trenogin, Teoriya vetvleniya resheniĭ nilineĭnykh uravneniĭ, Izdat. “Nauka”, Moscow, 1969 (Russian). MR 0261416

R. S. Varga, Functional analysis and approximation theory in numerical analysis, Conference Board of the Mathematical Sciences Regional Conference Series in Applied Mathematics, No. 3, Society for Industrial and Applied Mathematics, Philadelphia, Pa., 1971. MR 0310504

1.

M. Altman, Approximation methods in functional analysis, Lecture note, California Institute of Technology, Pasadena, Calif., 1959.

2.

P. M. Anselone, Collectively compact operator approximation theory, Prentice-Hall, Englewood Cliffs, N. J., 1971. MR 0443383

3.

J.-P. Aubin, Approximation of elliptic boundary-value problems, Interscience, New York, 1972. MR 478662

3a. E. Bishop, Foundations of constructive analysis, McGraw-Hill, New York, 1967. MR 36 #4930; See also the review by G. Stolzenberg, Bull. Amer. Math. Soc. 76 (1970), 301-323. MR 257687




4.

E. K. Blum, Numerical analysis and computation: theory and practice, Addison-Wesley, Reading, Mass., 1972. MR 408185

5.

H. Brezis, Opérateurs minimaux monotones et semigroups de contractions dans les espaces de Hilbert, North-Holland Math. Studies, no. 5, North-Holland, Amsterdam; American Elsevier, New York, 1973. MR 50 #1060. MR 348562

6.

F. E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Proc. Sympos. Pure Math., vol. 18, part 2, Amer. Math. Soc., Providence, R. I., 1976. MR 405188

7.

L. Collatz, Funktional analysis und numerische Mathematik, Springer-Verlag, Berlin, 1964; English transl., Functional analysis and numerical mathematics, Academic Press, New York, 1966. MR 29 #2931; 34 #4961. MR 165651

8.

J. Cronin-Scanlon, Fixed points and topological degree in nonlinear analysis, Math. Surveys, no. 11, Amer. Math. Soc., Providence, R. I., 1964. MR 29 #1400. MR 164101

9.

J. D. Daniel, The approximate minimization of functional, Prentice-Hall, Englewood Cliffs, N. J., 1971. MR 42 #7279. MR 272398

10.

V. F. Demyanov and A. M. Rubinov, Approximate methods in optimization problems, Izdat. Leningrad Univ., Leningrad, 1968; English transl., American Elsevier, New York, 1970. MR 39 #6137; 42 #927. MR 266018

11.

P. L. Falb and J. L. de Jong, Some successive approximation methods in control and oscillation theory, Academic Press, New York, 1969. MR 41 #9446. MR 264855

12.

A. A. Goldstein, Constructive real analysis, Harper & Row, New York, 1967. MR 36 #705. MR 217616

13.

L. V. Kantorovič, The method of successive approximations for functional equations, Acta Math. 71 (1939), 63-97. MR 1, 18.

14.

L. V. Kantorovič, Functional analysis and applied mathematics, Uspehi Mat. Nauk 3 (1948), no. 6 (28), 89-185; English transl., Nat. Bur. Standards Rep., no. 1509, U. S. Dept. of Commerce, Nat. Bur. Standards, Washington, D. C., 1952. MR 10, 380; 14, 766. MR 27947

15.

L. V. Kantorovič and G. P. Akilov, Functional analysis in normed spaces, Fizmatgiz, Moscow, 1959; German transl., Akademie-Verlag, Berlin, 1964; English transl., Macmillan, New York, 1964. MR 22 #9837; 31 #1536; 35 #4699. MR 213845

16.

M. A. Krasnosel'skiĭ, Topological methods in the theory of nonlinear integral equations, GITTL, Moscow, 1956; English transl., Macmillan, New York, 1964. MR 20 #3464; 28 #2414. MR 159197

17.

M. A. Krasnosel'skiĭ, Positive solutions of operator equations, Fizmatgiz, Moscow, 1962; English transl., Noordhoff, Groningen, 1964. MR 26 #2862; 31 #6107. MR 181881

18.

M. A. Krasnosel'skiĭ, G. M. Vaĭnikko, P. O. Zabreĭko, Ja. B. Rutickiĭ and V. Ja. Stecenko, Approximate solution of operator equations, "Nauka", Moscow, 1969; English transl., Wolters-Noordhoff, Groningen, 1972. MR 41 #4271. MR 385655

19.

M. S. Kurpel, Projection-iterative methods for solution of operator equations, "Naukova Dumka", Kiev, 1968; English transl., Transl. Math. Monographs, Amer. Math. Soc., Providence, R. I. (to appear). MR 254691

20.

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21.

S. G. Mihlin, The numerical performance of variational methods, "Nauka", Moscow, 1966; English transl., Wolters-Noordhoff, Groningen, 1971. MR 34 #3747; 43 #4236. MR 278506

22.

M. Z. Nashed, Differentiability and related properties of nonlinear operators: Some aspects of the role of differentials in nonlinear functional analysis, Nonlinear Functional Anal. and Appl. (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970), Academic Press, New York, 1971, pp. 103-309. MR 43 #2580. MR 276840

23.

M. Z. Nashed, Generalized inverses, normal solvability, and iteration for singular operator equations (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1970), Academic Press, New York, 1971, pp. 311-359. MR 43 #1003. MR 275246

24.

M. Z. Nashed, (editor), Generalized inverses and applications (Proc. Advanced Sem., Math. Res. Center, Univ. of Wisconsin, Madison, Wis., 1973), Academic Press, New York, 1976. MR 451661

25.

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26.

J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York, 1970. MR 42 #8686. MR 273810

27.

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29.

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30.

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31.

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32.

J. T. Schwartz, Nonlinear functional analysis, Gordon and Breach, New York, 1969. MR 433481

33.

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