Book Reviews

Linear Algebra, 2nd edition by Serge Lang (1971). Addison-Wesley Publishing Company.

Linear Algebra with Applications by Hugh G. Campbell. Appleton-Century-Crofts, New York, 1971. xiii + 396 pp. + A45.An Engineering Approach to Linear Algebra, by W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50)

An Engineering Approach to Linear Algebra, By W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50) Sparse Matrices, by R. P. Tewarson. ($11.95)

Sparse Matrices, by R. P. Tewarson. ($11.95)     

Book Reviews

Linear Algebra and Analytic Geometry, by H. W. Brinkmann and E. A. Klotz. Addison-Wesley, Reading, Mass., 1971.

Metric Affine Geometry, by Ernst Snapper and Robert J. Troyer. Academic Press, New York, 1971. xx + 435 pp. ($13.50).

Metric Affine Geometry, by Ernst Snapper and Robert J. Troyer. Academic Press, New York, 1971. xx + 435 pp. ($13.50)

Studies in Pure Mathematics, papers presented to Richard Rado. Edited by L. Mirsky, Academic Press, 1971, vii + 276 pp. (£5.00)

Linear Algebra (2nd edition), by Hoffmann and Kunze.

Linear Algebra, by Georgi E. Shilov. Translated by Richard A. Silverman.

Linear Algebra, by Georgi E. Shilov. Translated by Richard A. Silverman.     

Book Reviews

Linear Algebra, 2nd edition by Serge Lang (1971). Addison-Wesley Publishing Company.

Linear Algebra with Applications by Hugh G. Campbell. Appleton-Century-Crofts, New York, 1971. xiii + 396 pp. + A45.An Engineering Approach to Linear Algebra, by W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50)

An Engineering Approach to Linear Algebra, By W. W. Sawyer. Cambridge University Press, Cambridge, 1972. 304 pp. ($11.50) Sparse Matrices, by R. P. Tewarson. ($11.95)

Sparse Matrices, by R. P. Tewarson. ($11.95)     

Book Reviews

Elements of The Theory of Representations, by A. A. Kirillov (translated from the Russian by Edwin Hewitt) (Grundlehren der mathematischen Wissenschaften No. 220). Springer-Verlag, Berlin-Heidelberg-New York, 1976. xi+315 pp.

Charting The Operator Domain, by John Ernest. Amer. Math. Soc, 207 pp.

Ergodic Theory: A Seminar, by J. Moser, E. Phillips and S. Varadhan. New York University Press, 131 pp, $3.50.     

Book Reviews

Theory of Operator Algebras I by Maramichi Takesaki. Springer Verlag New York Inc., 1979

An Introduction to Stochastic Processes by D. Kannan, North Holland, New York, 1979, xii + 296 pp., $24.50.     

Book Reviews

Methods of Intermediate Problems for Eigenvalues: Theory and Ramifications, by Alexander Weinstein and William Stenger. Academic Press, 1971. ($16.00)

Combinatorics, Proceedings of the British Combinatorial Conference 1973, Edited by T.P. McDnough and V.C. Mavron, London Mathematical Society Lecture Note Series 13, Cambridge University Press, London, New York, 1974. 204pp.($9.95)     

Book Reviews

Finite Dimensional Linear Analysis: A Systematic Presentation in Problem Form,by I.M. Glazman and Ju. I. Ljubic, translated and edited by G.P. Barker and G.Kuerti. MIT Press, 520 pp.($18.50)

An Introduction to Linear Algebra, by Hans Samelson. John Wiley & Sons, New York, 1974 xi+265pp.($15.95).     

Book reviews

INtroduction to Group Characters, by Lederman, L.A.M.A., Cambridge University Press, 1977.

Matrix Representations in the Theory of Finite Groups, by V. A. Belonogov and A. N. Fomin. Nauka, Moscow, 1976 (in Russian). 48 kopecks.

Transformation Groups, Czes Kosniowski, Editor. London Mathematical Society Lecture Notes 26. Cambridge University Press, New York, 1977.     

Book Reviews

A Primer of Linear Algebra, by Gerald L. Bradley, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1975, 350 pp.

Banach Algebras, by Richard D. Mosak, University of Chicago Press, (Cloth: $9.00; Paper: $3.95).     

Book Reviews

Commutative Rings, by Irving Kaplansky. Revised edition. The University of Chicago Press, Chicago and London, 1974, ix+182pp.($9.75)

Symmetry Groups and their Applications, by Willard Miller, Jr. Academic Press.     

Book review

Linear numerical analysis, by Noël Gastinel. Hermann, Paris, 1970. 341 pp.

Linear determinants with applications to the picard scheme of a family of algebraic curves, by Birger Iversen (Lecture Notes in Maths., VoI. 174). Springer; 1970. vi + 69 pp. ($2.20)

Invariant theory old and new, by Jean A. DieudonnC and James B. Carrell. Academic Press, 1973.

Introduction to matrix analysis (2nd Edition), by Richard Bellman. McGraw-Hill, 1970. 403 pp     

Book reviews

An Introduction to Abstract Algebra, by Thomas A. Whitelaw. The Blackie Group of Publishers. Glasgow, United Kingdom, March 1978. 176pp.

Managerial Planning: An Optimum and Stochastic Control Approach (two volumes: Vol I: xxi + 240pp. and vol 2: x +241-642 pp.), by Charles S. Tapiero. London and New York: Gordon and Breach, 1977     

A Generalized φ-Divergence for Asymptotically Multivariate Normal Models

I. Csiszár's (Magyar. Tud. Akad. Mat. Kutató Int. Közl8 (1963), 85–108) -divergence, which was considered independently by M. S. Ali and S. D. Silvey (J. R. Statist. Soc. Ser. B28 (1966), 131–142) gives a goodness-of-fit statistic for multinomial distributed data. We define a generalized φ-divergence that unifies the -divergence approach with that of C. R. Rao and S. K. Mitra (“Generalized Inverse of Matrices and Its Applications,” Wiley, New York, 1971) and derive weak convergence to a χ² distribution under the assumption of asymptotically multivariate normal distributed data vectors. As an example we discuss the application to the frequency count in Markov chains and thereby give a goodness-of-fit test for observations from dependent processes with finite memory.     

Book Reviews

Numerical Ranges of Operators on Normed spaces and of elements of Normed Algebras, by F. F. Bonsall and J. Duncan. (London Mathematical Society Lecture Note, Series, 2). Cambridge University Press, 1971. ($3.95) Numerical RangesII, by F. F. Bonsall and J. Duncan. (London Mathematical Society Lecture Note, Series, 10). Cambridge University Press, 1973. ($7.50) Latent roots and latent vectors, by S.J. Hammerling ($13.50)

Latent Roots and Latent Vectors, by S.J. Hammerling. ($13.50)     

Short Book Reviews

Matrix Groups, by Morton L. Curtis, Springer Verlag Universitext, 1979.

Linear Algebra and Some of its Applications, by L. I. Golovina, Moscow (Nauka), 1979.     

Short Book Reviews

Problems in Linear Algebra, by I. V. Proskuryakov. Mir Publishers, Moscow, 1978= 453 pp.

Inequalities: Theory of Majorization and its Applications. by A. W. Marshall and I. Olkin. Academic Press, 1979, 569 pp.

Problems in Linear Algebra, by I. V. Proskuryakov. Mir Publishers, Moscow, 1978. 453 pp. Inequalities: Theory of Majorization and its Applications. by A. W. Marshall and I. Olkin. Academic Press, 1979, 569 pp. Introduction to Numerical Analysis. by F. Stummel and K. Hainer. Scottish Academic Press (in United States, Columbia University Press), 1980. 282 pp., soft cover.

Introduction to Numerical Analysis. by F. Stummel and K. Hainer. Scottish Academic Press (in the United States, Columbia University Press), 1980. 282 pp., soft cover.     

Book reviews

Rings with Involution By. I.N.Herstein.University of Chicago Press. 247 pp. ($5.50).

Improperly posed Boundary value Problems By a. Carasso and A.P. Stone. Pitman Publishing, San Francisco, 1975.($12.90).     

Stochastic evolution equations. Linear Theory and Applications to Nonlinear Filtering

Stochastic evolution equations. Linear Theory and Applications to Nonlinear Filtering, by B. L, Rozovskii. Kluwer, Dordrecht/Boston/London, March 1991. 336 pp., $129. ISBN 0-7923-00370-8.

Stochastic equations in infinite dimensions Stochastic equations in infinite dimensions, by G. Da Prato & J. Zabczyk. Cambridge University Press, Port Chester/New York, March 1993. 454 pp., $89.95. ISBN 0-541-38529-6     

On a class of Newton-like methods for solving nonlinear equations

We provide a semilocal convergence analysis for a certain class of Newton-like methods considered also in [I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374–397; I.K. Argyros, Computational theory of iterative methods, in: C.K. Chui, L. Wuytack (Eds.), Series: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co, New York, USA, 2007; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971], in order to approximate a locally unique solution of an equation in a Banach space.     

Book reviews

L.N. TREFETHEN and D. BAU, III,Numerical Linear Algebra,SIAM, Philadelphia, 1997G.-C. ROTA,Indiscrete Thoughts,Birkhäuser, Boston, 1997D.E. KEYES, A. SAMEH and V. VENKATAKRISHNAN, eds.Parallel Numerical Algorithms,Kluwer, Dordrecht, 1997A. KIRSCH,An Introduction to the Mathematical Theory of Inverse Problems,Springer, New York, 1996L.F. SHAMPINE, R.C. ALLEN, Jr. and S. PRUESS,Fundamentals of Numerical Computing,Wiley, New York, 1997C.W. UEBERHUBERNumerical Computation, 2 vols.Springer, Berlin, 1997W.G. McCALLUM et al.Multivariate Calculus,Wiley, New York, 1997ZHI-QUAN LUO, JONG-SHI PANG and D. RALPH,Mathematical Programs with Equilibrium Constraints,Cambridge University Press, Cambridge, 1996P.R. POPIVANOV and D.K. PALAGACHEV,The Degenerate Oblique Derivative Problem for Elliptic and Parabolic Equations,Akademie Verlag, Berlin, 1997