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Fundamentals of pattern recognition
Mathematics and Computers in Simulation 31 (1989) 283-295 North-Holland
BOOK REVIEWS
283
*
Edited by W.F. AMES and C. BREZINSKI
D.H. Griffel, Linear Algebra and Its Applications, Ellis Horwood Ltd., Chichester, 1989. Vol. 1: ISBN o-85312-946-0, XIII + 289 pages, 229.95. Vol. 2: ISBN o-7458-0581-7, X + 233 pages, 229.95. These two volumes cover the classical and advanced topics that students must know on finite-dimensional spaces. Volume 1 is devoted to vector spaces, matrices, linear equations and linear transformations. The second volume deals with matrix representations and diagonalisation, inner products and self-adjoint operators and further developments such as least squares, duality and linear programming. I found these books particularly clear and well written. There are many examples to help the reader understanding the theoretical concepts and theorems. Remarks and exercises are also very valuable and the presentation is pleasant. (CB) R.P. Agarwal, Y.M. Chow and S.J. Wilson (Eds), Numerical Mathematics, Singapore, 1988. ISNM Vol. 86, Birkhauser, Basel, 1989. ISBN 3-7643-2255-1, XIII + 526 pages, SFr. 118. This book contains the talks given at an international conference on numerical mathematics held in Singapore from May 31 to June 4, 1988 where some 160 mathematicians from 30 countries attended. The topics covered by the 42 original papers are discrete mathematics, ordinary and partial differential equations, integral equations, quadratures, special functions, extrapolation, mathematical modelling, multivariate polynomial equations, approximation, control, parallel computing, linear algebra, and engineering applications. (CB) M. Pavel, Fundamentals of Pattern Recognition, 8025-6, IX + 183 pages.
Marcel Dekker, New York, 1989. ISBN O-8247-
The major concern of this book is to give a precise mathematical treatment of pattern recognition. Chapter 2 deals with the fundamental problems of pattern recognition which are classification and recognition. Chapter 3 treats the topological framework for images and shapes. Chapter 4 is devoted to the structural framework since “reality can be grasped in all its * Books for review should be sent to Professor W.F. Ames (subjects: modeling, partial differential equations, differential equations, applied mathematics) or Professor C. Brezinski (subjects: interpolation, quadrature, approximation theory, linear algebra, history and philosophy of mathematics). The postal addresses are given on the inside front cover. (RV = Professor R. Vichnevetsky, Editor-in-Chief.) 0378-4754/89/$3.50
0 1989, Elsevier Science Publishers B.V. (North-Holland)
284
Book Reviews
complexity only by a descriptive approach”. The last chapter gives a general formalism of the recognition problem. This book is widely based on Mrs. Pavel’s own work. It will be a valuable reference for applied mathematicians, computer scientists, electrical and electronic engineers, system analysts and engineers. It can also be used as a text book for graduate students and those desiring to begin research in this domain. (CB) J. Haslinger and P. Neittaanmiiki, Finite Element Approximation for Optimal Shape Design, Theory and Applications, J. Wiley, Chichester, 1988. ISBN o-471-92079-7, XII + 335 pages, &35. This book deals with the mathematical formulation, the finite element approximation and the numerical solution of optimal shape design problems. The aim is to computerize the design process in order to create new shapes or to improve an existing design. The subject, which has many applications in CAD, is at the interface of optimal control, partial differential equations, numerical analysis and optimization theory. The first chapters of the book formulate the problems posed by optimal shape design while the subsequent chapters describe the methods for their solution. Emphasis is placed on problems governed by elliptic variational inequalities and on the finite element method. Examples of calculations are given and the appendices contain algorithms. This book will be useful to engineers and applied mathematicians. (CB) B. Sendov and V.A. Popov, The Awraged Moduli ISBN O-471-91952-7, X + 181 pages, E24.95.
of Smoothness,
J. Wiley, Chichester,
1988.
Many numerical methods provide approximations. In particular this is the case in interpolation, approximation of functions by means of operators, quadrature formulae, spline approximations, and network methods for the numerical solution of integral and differential equations. This book presents the theory and the applications of a new method of estimating the error in commonly used numerically methods such as those described above. This new method, called the averaged moduli of smoothness, is based on a new characteristic of functions and it allows to estimate the error without making any assumptions about the function involved beyond those imposed by the problem itself. This book provides the theory and many applications of the method. It makes available for the first time in English and in book form, many results which were either difficult to find or in Russian. It will become a valuable reference to numerical analysts. (CB) H.O. Peitgen and D. Saupe (Eds), The Science of Fractal Images, Springer-Verlag, Berlin, 1988. ISBN 3-540-96608-0, XIV + 312 pages, DM 69. This is the book that those desiring to learn the mathematics behind fractals must acquire. It is based on lectures given by recognized leaders in the field. The chapters are the following: ‘People ‘Fractals in nature: from and events behind the “science of fractal images”’ by B.B. Mandelbrot; for random fractals’ by D. Saupe; characterization to simulation’ by R.F. Voss; ‘Algorithms ‘Fractal patterns arising in chaotic dynamical systems’ by R.L. Devaney; ‘Fractal modelling of
BOOK REVIEWS
283
*
Edited by W.F. AMES and C. BREZINSKI
D.H. Griffel, Linear Algebra and Its Applications, Ellis Horwood Ltd., Chichester, 1989. Vol. 1: ISBN o-85312-946-0, XIII + 289 pages, 229.95. Vol. 2: ISBN o-7458-0581-7, X + 233 pages, 229.95. These two volumes cover the classical and advanced topics that students must know on finite-dimensional spaces. Volume 1 is devoted to vector spaces, matrices, linear equations and linear transformations. The second volume deals with matrix representations and diagonalisation, inner products and self-adjoint operators and further developments such as least squares, duality and linear programming. I found these books particularly clear and well written. There are many examples to help the reader understanding the theoretical concepts and theorems. Remarks and exercises are also very valuable and the presentation is pleasant. (CB) R.P. Agarwal, Y.M. Chow and S.J. Wilson (Eds), Numerical Mathematics, Singapore, 1988. ISNM Vol. 86, Birkhauser, Basel, 1989. ISBN 3-7643-2255-1, XIII + 526 pages, SFr. 118. This book contains the talks given at an international conference on numerical mathematics held in Singapore from May 31 to June 4, 1988 where some 160 mathematicians from 30 countries attended. The topics covered by the 42 original papers are discrete mathematics, ordinary and partial differential equations, integral equations, quadratures, special functions, extrapolation, mathematical modelling, multivariate polynomial equations, approximation, control, parallel computing, linear algebra, and engineering applications. (CB) M. Pavel, Fundamentals of Pattern Recognition, 8025-6, IX + 183 pages.
Marcel Dekker, New York, 1989. ISBN O-8247-
The major concern of this book is to give a precise mathematical treatment of pattern recognition. Chapter 2 deals with the fundamental problems of pattern recognition which are classification and recognition. Chapter 3 treats the topological framework for images and shapes. Chapter 4 is devoted to the structural framework since “reality can be grasped in all its * Books for review should be sent to Professor W.F. Ames (subjects: modeling, partial differential equations, differential equations, applied mathematics) or Professor C. Brezinski (subjects: interpolation, quadrature, approximation theory, linear algebra, history and philosophy of mathematics). The postal addresses are given on the inside front cover. (RV = Professor R. Vichnevetsky, Editor-in-Chief.) 0378-4754/89/$3.50
0 1989, Elsevier Science Publishers B.V. (North-Holland)
284
Book Reviews
complexity only by a descriptive approach”. The last chapter gives a general formalism of the recognition problem. This book is widely based on Mrs. Pavel’s own work. It will be a valuable reference for applied mathematicians, computer scientists, electrical and electronic engineers, system analysts and engineers. It can also be used as a text book for graduate students and those desiring to begin research in this domain. (CB) J. Haslinger and P. Neittaanmiiki, Finite Element Approximation for Optimal Shape Design, Theory and Applications, J. Wiley, Chichester, 1988. ISBN o-471-92079-7, XII + 335 pages, &35. This book deals with the mathematical formulation, the finite element approximation and the numerical solution of optimal shape design problems. The aim is to computerize the design process in order to create new shapes or to improve an existing design. The subject, which has many applications in CAD, is at the interface of optimal control, partial differential equations, numerical analysis and optimization theory. The first chapters of the book formulate the problems posed by optimal shape design while the subsequent chapters describe the methods for their solution. Emphasis is placed on problems governed by elliptic variational inequalities and on the finite element method. Examples of calculations are given and the appendices contain algorithms. This book will be useful to engineers and applied mathematicians. (CB) B. Sendov and V.A. Popov, The Awraged Moduli ISBN O-471-91952-7, X + 181 pages, E24.95.
of Smoothness,
J. Wiley, Chichester,
1988.
Many numerical methods provide approximations. In particular this is the case in interpolation, approximation of functions by means of operators, quadrature formulae, spline approximations, and network methods for the numerical solution of integral and differential equations. This book presents the theory and the applications of a new method of estimating the error in commonly used numerically methods such as those described above. This new method, called the averaged moduli of smoothness, is based on a new characteristic of functions and it allows to estimate the error without making any assumptions about the function involved beyond those imposed by the problem itself. This book provides the theory and many applications of the method. It makes available for the first time in English and in book form, many results which were either difficult to find or in Russian. It will become a valuable reference to numerical analysts. (CB) H.O. Peitgen and D. Saupe (Eds), The Science of Fractal Images, Springer-Verlag, Berlin, 1988. ISBN 3-540-96608-0, XIV + 312 pages, DM 69. This is the book that those desiring to learn the mathematics behind fractals must acquire. It is based on lectures given by recognized leaders in the field. The chapters are the following: ‘People ‘Fractals in nature: from and events behind the “science of fractal images”’ by B.B. Mandelbrot; for random fractals’ by D. Saupe; characterization to simulation’ by R.F. Voss; ‘Algorithms ‘Fractal patterns arising in chaotic dynamical systems’ by R.L. Devaney; ‘Fractal modelling of