Skip to Content

TURING, A. M.

Rounding-off Errors in Matrix Processes. - [TURING'S LU FACTORIZATION]

Herman H. J. Lynge & Søn A/S
lyn47095
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.
Address:
Silkegade 11
DK-1113 Copenhagen
Denmark
Phone:
CVR/VAT:
DK 16 89 50 16

Recently Added From Herman H. J. Lynge & Søn A/S

Orations on Philosophy and Education. (Cambridge…
More Photos
MELANCHTHON, PHILIP. - SACHIKO KUSUKAWA (ED.) & CHRISTINE F. SALAZAR (TRANSL.)
Herman H. J. Lynge & Søn A/S
lyn62729
Cambridge University Press, 1999. 8vo. Hardback. Slight wear to capitals. Ownership signature and notes in pencil to inside of front board. A few scattered marginal notes and underlinings in text in pencil. XXXIX, 272 pp.
Vorträge und Aufsätze.  - [PRESENTATION-COPY OF…
More Photos
HEIDEGGER, MARTIN.
Herman H. J. Lynge & Søn A/S
lyn62680
Pfullingen, Günter Neske, (1954). 8vo. Original full black cloth with white lettering to spine. Very clean, bright, and fresh, also internally. Original orange dust-jacket with black lettering to spine and white lettering to front. Minimal edge wear. An excellent and clean dust-jacket with just minor signs of wear. Very slight soiling to title-page, otherwise no wear or markings to text. Letter from Heidegger inserted to inside of front board. Front free end-paper signed and dated by Heidegger and with an inserted note in ink from the person that Heidegger gave the book to stating that this highly personal memento from his student time in Freiburg and his memorable encounters with Heidegger was given to his son Matthias for his 40th birthday, in 1995. 283, (1) pp. First edition, presentation-copy signed by Heidgger and with an inserted letter, also signed and dated by Heidegger, of this seminal collection of lectures and essays, which was of decisive importance to the immense influence of Heidegger’s thinking upon post World War Europe. This collection of Heidegger’s lectures and essays contains such groundbreaking works as “Die Frage nach der Technik” (The Question Concerning Technology) and “Wissenschaft und Besinnung” (Science and Reflection), “”Dichterisch Wohnet der Mensch…” “, along with other important works written between 1936 and 1953 collected here for the first time. This collection would later be reprinted and serve as volume 7 of Heidegger’s collected works (the Gesamtausgabe). This copy is signed “Martin Heidegger” and dated (1954 – the year of publication) to the front free end-paper, and on the inside of the front board is inserted an autograph signed letter in Heidegger’s hand to “Sehr geehrter Herr Doktor” (honourable doctor), in which Heidegger asks to meet up the following day, suggesting different times of the day. The letter is dated Freiburg 10th of February, 1954, which is two days before Heidegger gave his groundbreaking lecture “The Question Concerning Technology” at the University of Freiburg, suggesting that the letter was given to someone attending the lecture, possibly someone with whom he wanted to discuss it beforehand. “The Question Concerning Technology” still serves as one of the most pertinent philosophical essays of modern time, foreshadowing what is arguably the greatest philosophical and moral dilemmas that we struggle with today due to modern technology. Heidegger begins with asking the question what technology is, in an attempt to fully understand its essence and to ultimately prepare a free relationship to it – a theme that could hardly be more relevant today. “As relevant now as ever before, this accessible collection is an essential landmark in the philosophy of science from one of the most profound thinkers of the twentieth century (New York Times). The advent of machine technology has given rise to some of the deepest problems of modern thought. Featuring the celebrated essay The Question Concerning Technology, this prescient volume contains Martin Heidegger's groundbreaking investigation into the pervasive enframing character of our understanding of ourselves and the world.” (Harper Collins: The Question Concerning Technology And Other Essays By Martin Heidegger, 2013). “Science and Reflection” (here published for the first time), a lecture delivered on August 4, 1953, to a small circle of attendees, is Heidegger’s meditation on the difference between science and “mindfulness”, and an as-relevant-as-ever attempt at uniting science as such, in itself, with its application and meaning, combatting scientific fragmentation. In line with the other foreshadowing lectures, “Dichterisch wohnet der Mensch”, given on October 6, 1951, in Bühlerhöhe, seeks to explore how to reach a peace or dwelling in a modern, technological world. Heidegger uses the quote by Hölderlin to explore how human existence is deeply intertwined with language and poetry and reaches the conclusion that to truly dwell is to live in a poetic way, allowing for the meaningful unfolding of the world through language. The other essays/lectures printed in this seminal volume are: Überwindung der Metaphysik (1936-1946) Wer ist Nietzsches Zarathustra (1953) Was heißt Denken? (1952) Bauen Wohnen Denken (1951) Das Ding (1950) Logos (Heraklit, Fragment 50) (1951) Moira (Parmenides, Fragment VIII, 34-41) (1952) Aletheia (Heraklit, Fragment 16) (1954)
More info
On Tycho's Island. Tycho Brahe and His…
More Photos
CHRISTIANSON, JOHN ROBERT.
Herman H. J. Lynge & Søn A/S
lyn62730
Cambridge University Press, 2000. 8vo. In the original blue cloth publisher's binding with gilt title to spine and front board. With the original dust jacket. Insignificant wear to capitals. Ownership signature to inside of front board. Internally clean. XII, 451 pp.
A Holy Commonwealth. Edited by William Lamont.
More Photos
BAXTER, RICHARD. - WILLIAM LAMONT (ED.)
Herman H. J. Lynge & Søn A/S
lyn62731
Cambridge University Press, 1994. 8vo. In the original red cloth publisher's binding with gilt title to spine. With the original dust jacket. Ownership signature to inside of front board. Internally clean. XXXI, 254, (2) pp.
Entretiens sur la pluralité des mondes.
More Photos
FONTENELLE
Herman H. J. Lynge & Søn A/S
lyn62726
Dijon, Imprimerie de P Causse, An 2 (1793). 8vo. In contemporary half calf. Wear to extremities. Ex-libris pasted down to pasted down front end-paper and previous owner's name to front free end-paper. First and last leaves with light browning and a small stain to upper margin, but generally internally nice and clean. (4), 291 pp.
Hellige Taler, udgivne til Bedste for de, ved…
More Photos
SMITH, L.
Herman H. J. Lynge & Søn A/S
lyn62722
Fridericia, Kongl. privil. Adressecontoirs Bogtrykkerie, 1787. 8vo. In contemporary full sprinkled calf with five raised bands and richly gilt spine. Edges of boards with wear and leather on spine cracked. (32), 368, (1) pp. First edition of this scarce publication issued in the aftermath of the catastrophic Vejle fire of 23 April 1786, which destroyed much of the town. The book is a collection of religious sermons, published with the purpose of raising funds to aid the impoverished citizens of Vejle who had lost their homes and livelihoods in the fire.
More info