Everand Logo

Welcome to Everand!

  • Discover millions of ebooks, audiobooks, and so much more with a free trial

    Only $11.99/month after trial. Cancel anytime.

    Solution of Equations and Systems of Equations: Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 9
    Solution of Equations and Systems of Equations: Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 9
    Solution of Equations and Systems of Equations: Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 9
    Ebook278 pages5 hours

    Solution of Equations and Systems of Equations: Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 9

    By A. M. Ostrowski and Samuel Eilenberg

    ()

    Read preview

    About this ebook

    Solution of Equations and Systems of Equations, Second Edition deals with the Laguerre iteration, interpolating polynomials, method of steepest descent, and the theory of divided differences. The book reviews the formula for confluent divided differences, Newton's interpolation formula, general interpolation problems, and the triangular schemes for computing divided differences. The text explains the method of False Position (Regula Falsi) and cites examples of computation using the Regula Falsi. The book discusses iterations by monotonic iterating functions and analyzes the connection of the Regula Falsi with the theory of iteration. The text also explains the idea of the Newton-Raphson method and compares it with the Regula Falsi. The book also cites asymptotic behavior of errors in the Regula Falsi iteration, as well as the theorem on the error of the Taylor approximation to the root. The method of steepest descent or gradient method proposed by Cauchy ensures "global convergence" in very general conditions.

    This book is suitable for mathematicians, students, and professor of calculus, and advanced mathematics.

    LanguageEnglish
    PublisherAcademic Press
    Release dateJun 3, 2016
    ISBN9781483223643
    Solution of Equations and Systems of Equations: Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 9

    Related to Solution of Equations and Systems of Equations

    Related ebooks

    Mathematics For You

    View More
    View More

    Related podcast episodes

    Related articles

    • Article

      How Physics Is Like Three-Chord Rock: Like a set of common chords, the same math appears in diverse fields of physics.

      Jun 12, 2014

      A few years back, 12 million of us clicked over to watch the “Pachelbel Rant” on YouTube. You might remember it. Strumming repetitive chords on his guitar, comedian Rob Paravonian confessed that when he was a cellist, he couldn’t stand the Pachelbel

      6 min read

    • Article

      A Supermassive Lens On The Constants Of Nature

      Nov 25, 2020

      The 2020 Nobel Prize in Physics went to three researchers who confirmed that Einstein’s general relativity predicts black holes, and established that the center of our own galaxy houses a supermassive black hole with the equivalent of 4 million suns

      9 min read

    • Article

      The Math That Takes Newton Into the Quantum World

      Feb 28, 2019

      In my 50s, too old to become a real expert, I have finally fallen in love with algebraic geometry. As the name suggests, this is the study of geometry using algebra. Around 1637, René Descartes laid the groundwork for this subject by taking a plane,

      9 min read

    • Article

      How Math’s Most Famous Proof Nearly Broke

      Dec 20, 2018

      Andrew Wiles gave a series of lectures cryptically titled “Modular Forms, Elliptic Curves, and Galois Representations” at a mathematics conference in Cambridge, England, in June 0f 1993. His argument was long and technical. Finally, 20 minutes into t

      8 min read

    • Article

      How Math’s Most Famous Proof Nearly Broke: Andrew Wiles thought he had a solution to an age-old puzzle. Until it began to unravel.

      May 28, 2015

      Andrew Wiles gave a series of lectures cryptically titled “Modular Forms, Elliptic Curves, and Galois Representations” at a mathematics conference in Cambridge, England, in June 0f 1993. His argument was long and technical. Finally, 20 minutes into t

      8 min read

    • Article

      Physicists Attack Math’s $1,000,000 Question

      Apr 4, 2017

      Physicists are attempting to map the distribution of the prime numbers to the energy levels of a particular quantum system.

      4 min read

    • Article

      The Deepest Uncertainty: When a hypothesis is neither true nor false.

      Jun 6, 2013

      Georg Cantor died in 1918 in a sanatorium in Halle, Germany. A pre-eminent mathematician, he had laid the foundation for the theory of infinite numbers in the 1870s. At the time, his ideas received hostile opposition from prominent mathematicians in

      4 min read

    • Article

      The Universe Began With a Big Melt, Not a Big Bang

      Oct 5, 2017

      There are two tantalizing mysteries about our universe, one dealing with its final fate and the other with its beginning, that have intrigued cosmologists for decades. The community has always believed these to be independent problems—but what if the

      10 min read

    • Article

      The Deepest Uncertainty

      May 16, 2019

      Georg Cantor died in 1918 in a sanatorium in Halle, Germany. A pre-eminent mathematician, he had laid the foundation for the theory of infinite numbers in the 1870s. At the time, his ideas received hostile opposition from prominent mathematicians in

      4 min read

    • Article

      Roger Penrose

      Oct 6, 2022

      Roger Penrose
      1 min read

    • Article

      The Impossible Mathematics of the Real World

      Feb 21, 2019

      Using stiff paper and transparent tape, Craig Kaplan assembles a beautiful roundish shape that looks like a Buckminster Fuller creation or a fancy new kind of soccer ball. It consists of four regular dodecagons (12-sided polygons with all angles and

      6 min read

    • Article

      The Impossible Mathematics of the Real World

      Jun 8, 2017

      Using stiff paper and transparent tape, Craig Kaplan assembles a beautiful roundish shape that looks like a Buckminster Fuller creation or a fancy new kind of soccer ball. It consists of four regular dodecagons (12-sided polygons with all angles and

      6 min read

    • Article

      The Sacred, Spherical Cows of Physics: Theoretical physics milks symmetry to power its newest tool.

      May 1, 2014

      Early in their training, many physics students come across the idea of spherical cows. Cows in the real world—even at their most plump and well-fed—are hardly spherical, and this makes it tricky to calculate things like, say, how their volume or surf

      11 min read

    • Article

      Will Quantum Mechanics Swallow Relativity?: The contest between gravity and quantum physics takes a new turn.

      Oct 29, 2015

      It is the biggest of problems, it is the smallest of problems. At present physicists have two separate rulebooks explaining how nature works. There is general relativity, which beautifully accounts for gravity and all of the things it dominates: orbi

      17 min read

    Related categories

    Reviews for Solution of Equations and Systems of Equations

    0 ratings

    0 ratings0 reviews

    What did you think?

    Tap to rate

    Review must be at least 10 words

      Book preview

      Solution of Equations and Systems of Equations - A. M. Ostrowski

      Enjoying the preview?
      Page 1 of 1