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5 book(s) with the same title
Rounding-off Errors in Matrix Processes. - [TURING'S LU FACTORIZATION]
Oxford, Clarendon Press, 1948. 8vo. Bound in contemporary full calf with gilt lettering to spine. In ""The Quarterly Journal of Mechanics and Applied Mathematics"", Vol. 1, 1948. Previous owner's name written to front free-endpaper. Ver fine and clean. Pp. 287-380. [Entire volume: (4), 474 pp.].
First printing of this important paper in which Turing for the very first time introduced the concept of LU factorization or LU decomposition. ""Turing's paper was one of the earliest attempts to examine the error analysis of the various methods of solving linear equations and inverting matrices. His analysis was basically sound. The main importance of the paper was that it was published at the dawn of the modern computing era, and it gave indications of which methods were 'safe' when solving such problems on a computer"". (Burgoyne, Collected Works of A M Turing).""In 1945, [Turing] declined an offer of a Fellowship at King's [College, Cambridge] in favour of joining the newly formed Mathematical Division at the National Physical Laboratory (NPL). His early work on computability, combined with his wartime experience in electronics, had fired him with an enthusiasm for working on the design of an electronic computer. ethe machine he designed, which was called the Automatic Computing Engine (ACE) in recognition of Babbage's pioneering work, was characteristically original…""While in the Mathematics Division of NPL, Turing became keenly interested in numerical analysis. His paper, ""Rounding-off Errors in Matrix Processes"", showed that the acute anxiety about the effect of rounding errors in Gaussian elimination was largely unjustified. This paper has been overshadowed to some extent by the von Neumann and Goldstine paper on matrix inversion, but it is a brilliant piece of work and would have repaid closer study at the time"". (""Turing, Alan M."" by James H. Wilkinson, p. 1803, in Encyclopedia of Computer Science, A. Ralston et al (eds.), 4th edition, Nature Publishing Group, 2000).In linear algebra, LU decomposition factorizes a matrix as the product of a lower triangular matrix and an upper triangular matrix. LU decomposition is a key step in several fundamental numerical algorithms in linear algebra such as solving a system of linear equations, inverting a matrix, or computing the determinant of a matrix. Not in Origins of Cyberspace nor The Erwin Tomash Library.
Ein Beitrag zur Theorie des Legendre'schen Polynoms. - [HILBERT MATRIX]
Berlin, Stockholm, Paris, Almqvist & Wiksell, 1894. 4to. Bound in contemporary half cloth with gilt lettering to spine. In ""Acta Mathematica"", Vol, 18, 1894. Entire volume offered. Stamps to title page and light wear to extremities, otherwise a fine and clean copy. Pp. 155-59.[Entire volume: (4), 421, (2) pp].
First printing of Hilbert's paper in which he introduced The Hilbert Matrix. In linear algebra, a Hilbert matrix is a square matrix with entries being the unit fractions. The Hilbert matrix is symmetric and positive definite and is also totally positive (meaning the determinant of every submatrix is positive). The Hilbert matrix is an example of a Hankel matrix.
Matrix Computation for Engineers and Scientists
John Wiley and Sons Malicorne sur Sarthe, 72, Pays de la Loire, France 1978 Book condition, Etat : Bon hardcover, editor's full brown printed clothes, no dust-jacket grand In-8 1 vol. - 345 pages
Reprinted edition, 1978 Contents, Chapitres : Preface, Acknowledgments, Contents, xv, Text, 330 pages - Basic algebraic and numerical concepts - Some matrix problems - Storage schemes and matrix multiplication - Elimination methods for linear equations - Sparse matrix elimination - Iterative methods for linear equations - Some matrix eigenvalue problems - Transformation methods for eigenvalue problems - Sturm sequence methods - Vector iterative methods for eigenvalues - Appendices and index binding is in good condition, minor adhesive tracks on the bottom of the spine, without dust-jacket, few stamps and markings on the title-page, else near fine copy, text clean and unmarked, a very good reading copy
Die 'beobachtbaren' Grössen in der Theorie der Elementarteilchen (+) Die beobachtbaren Grössen in der Theorie der Elementarteilchen. II. - [THE DISCOVERY OF S-MATRIX]
Berlin, Springer, 1943. 8vo. In contemporary halv cloth with gilt lettering to spine. In ""Zeitschrift für Physik"", Bd. 120, 1943. Entire volume offered. Stamp to front free end-paper and titlepage, otherwise fine and clean. Pp. 513-538"" Pp. 673-702. [Entire volume: VII, (1), 790 pp.].
First printing of Heisenberg's two seminal paper on the scattering matrix, or S-matrix. """"S-matrix"" theory of particle scattering, especially in its later analytic forms, enjoyed considerable attention after the war, then again during the 1960's"" (DSB). These papers are ranked by David Cassidy as being amoung his most important.""The outbreak of world war in September 1939 profoundly affected Heisenberg and his career. Still of military age, he was ordered to report to the Army We apons Bureau (Heereswaffenamt) in Berlin. There the authorities asked him and other leading German nuclear physicists to investigate whether nuclear fission, discovered in Berlin a year earlier, could be used for large-scale energy production. Within two months Heisenberg completed a comprehensive report on the theory of chain reactions and their uses, including their use in an atomic bomb. Thereport made Heisenberg the leading specialist on nuclear energy in Germany.In order to continue the promising research, the Army Weapons Bureau designated the Kaiser Wilhelm Institute for Physics in Berlin the center of German fission research. After the departure of the institute's Dutchdirector, peter Debye, who chose emigration over German citizenship, Heisenberg was named adviser, and later acting director, of the institute and its nuclear research. At the same time, Heisenberg supervised preliminary reactor experiments in Leipzig. He also continued with high-energy interactions. In papers written between 1942 and 1944, Heisenberg developed a theory of particle collisions based, as in 1925, only upon the observable properties of the colliding particles. Theresulting ""S-matrix"" theory of particle scattering, especially in its later analytic forms, enjoyed considerable attention after the war, then again during the 1960's but renormalized field theories eventually found more followers."" (DSB)Cassidy 1943a, 1943b
Bullough (R.K.) and Caudrey (P.J.), eds. - G.L. Lamb and D.W. McLaughlin - H.M. Gibbs - M. Toda - R. Hirota - A.C. Newell - V.A. Zakharov - M. Wadali - F. Calogerro and A. Degasperis - S.P. Novikov - L.D. Faddeeev - A.H. Luther
Reference : 87855
(1980)
Solitons , Topics in Current Physics, volume 17 (The soliton and its history - Aspects of soliton physics - The double Sine-Gordon eqsuations: A physically applicable system of equations - On a nonlinear lattice, the Toda lattice - Direct methods in soliton theory - The inverse scattering transform - The inverse scattering method - Generalized matrix form of the inverse scattering method - Nonlinear evolution equations solvable by the inverse spectral transform associated with the matrix Schrödinger equation - A method of solving the periodic problem of the KdV equation and its generalizations -A Hamiltonian interpretation of the inverse scattering method - Quantum solitons in statistical physics)
Springer-Verlag - Springer , Topics in Current Physics Malicorne sur Sarthe, 72, Pays de la Loire, France 1980 Book condition, Etat : Bon hardcover, editor's brown and orange printed binding, issued without dust-jacket grand In-8 1 vol. - 408 pages
20 text-figures 1st Edition, 1980 Contents, Chapitres : Preface, Contents, List of Contributors, xviii, Texte, 390 pages - R.K. Bullouch and P.J. Caudrey : The soliton and its history - G.L. Lamb and D.W. McLaughlin : Aspects of soliton physics - R.K. Bullouch, P.J. Caudrey and H.M. Gibbs : The double Sine-Gordon eqsuations: A physically applicable system of equations - M. Toda : On a nonlinear lattice, the Toda lattice - R. Hirota : Direct methods in soliton theory - A.C. Newell : The inverse scattering transform - V.A. Zakharov : The inverse scattering method - M. Wadali : Generalized matrix form of the inverse scattering method - F. Calogerro and A. Degasperis : Nonlinear evolution equations solvable by the inverse spectral transform associated with the matrix Schrödinger equation - S.P. Novikov : A method of solving the periodic problem of the KdV equation and its generalizations - L.D. Faddeeev : A Hamiltonian interpretation of the inverse scattering method - A.H. Luther : Quantum solitons in statistical physics - NB : Un soliton est une onde solitaire qui se propage sans se déformer dans un milieu non linéaire et dispersif. On en trouve dans de nombreux phénomènes physiques de même qu'ils sont la solution de nombreuses équations aux dérivées partielles non linéaires. (source : Wikipedia) near fine copy, no markings
