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Sequence transformations
Mathematics and Computers North-Holland
BOOK
REVIEWS
in Simulation
31 (1989) 137-143
137
*
Edited by W.F. AMES and C. BREZINSKI J.P. Delahaye: “Sequence Transformations” (Volume 11, Springer Series in Computational Mathematics). Springer-Verlag, Berlin, 1988, 252 pp., DM 128, ISBN 3-540-15283-O. This book, intended for researchers, gives a clear concise summary of sequence transformations and convergence acceleration methods. Some of the features are precise definitions of algorithmic sequence transformations, the powers of sequence transformations, proof of negative results in acceleration methods (some sequence families are not accelerable), and new algorithms for convergence acceleration (automatic selection procedures). An introduction and historical survey is given by C. Brezinski. There is a modest bibliography and index. (WFA) J.P. Delahaye: “Sequence Transformations”, Springer Series in Computational Mathematics, 11. Springer-Verlag, New-York, ISBN o-387-15283-0, xxi + 252 pages, $79.50.
vol.
In numerical analysis one has often to deal with sequences either directly (fixed point iterations, summation of series, . _. ) or when the approximate solution of a problem depends on a parameter h and tends to the exact solution when h tends to zero and the computations are performed using a sequence (h,) converging to zero (differential equations, trapezoidal rule, . . .). In many cases such sequences converge too slowly and one has to use sequence transformations to accelerate them, a very crucial point. This book is a major contribution to the domain. Its author introduced many new and most powerful ideas such as the concept of remanence (which says when a set of sequences cannot be accelerated) and the optimal automatic selection of the best result among those given by several sequence transformations. This book will be a valuable reference not only to those working on extrapolation and convergence acceleration methods but also to those who need to use such methods in their work. (CB) S.O. Fatunla: “Numerical Methods for Initial Value Probtems in Ordinary Differential Equations” (Volume in Computer Science and Scientific Computing). Academic Press, San Diego, 1988, 295 pp., U.S. $44.50, ISBN 0-12-249930-l. Complementing the 1971 work of Gear and the 1973 book of Lambert this book emphasizes the numerical treatment of special differential equations. Included are stiff, stiff oscillatory, * 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)
BOOK
REVIEWS
in Simulation
31 (1989) 137-143
137
*
Edited by W.F. AMES and C. BREZINSKI J.P. Delahaye: “Sequence Transformations” (Volume 11, Springer Series in Computational Mathematics). Springer-Verlag, Berlin, 1988, 252 pp., DM 128, ISBN 3-540-15283-O. This book, intended for researchers, gives a clear concise summary of sequence transformations and convergence acceleration methods. Some of the features are precise definitions of algorithmic sequence transformations, the powers of sequence transformations, proof of negative results in acceleration methods (some sequence families are not accelerable), and new algorithms for convergence acceleration (automatic selection procedures). An introduction and historical survey is given by C. Brezinski. There is a modest bibliography and index. (WFA) J.P. Delahaye: “Sequence Transformations”, Springer Series in Computational Mathematics, 11. Springer-Verlag, New-York, ISBN o-387-15283-0, xxi + 252 pages, $79.50.
vol.
In numerical analysis one has often to deal with sequences either directly (fixed point iterations, summation of series, . _. ) or when the approximate solution of a problem depends on a parameter h and tends to the exact solution when h tends to zero and the computations are performed using a sequence (h,) converging to zero (differential equations, trapezoidal rule, . . .). In many cases such sequences converge too slowly and one has to use sequence transformations to accelerate them, a very crucial point. This book is a major contribution to the domain. Its author introduced many new and most powerful ideas such as the concept of remanence (which says when a set of sequences cannot be accelerated) and the optimal automatic selection of the best result among those given by several sequence transformations. This book will be a valuable reference not only to those working on extrapolation and convergence acceleration methods but also to those who need to use such methods in their work. (CB) S.O. Fatunla: “Numerical Methods for Initial Value Probtems in Ordinary Differential Equations” (Volume in Computer Science and Scientific Computing). Academic Press, San Diego, 1988, 295 pp., U.S. $44.50, ISBN 0-12-249930-l. Complementing the 1971 work of Gear and the 1973 book of Lambert this book emphasizes the numerical treatment of special differential equations. Included are stiff, stiff oscillatory, * 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)