Limit search to available items
Book Cover
E-book
Author Ostrowski, A. M. (Alexander Markowich), 1893-1986

Title Solution of equations and systems of equations [by] A.M. Ostrowski
Edition 2d ed
Published New York, Academic Press, 1966
Online access available from:
ProQuest Ebook Central    View Resource Record  

Copies

Description 1 online resource (xiv, 338 pages)
Series Pure and applied mathematics; a series of monographs and textbooks, 9
Pure and applied mathematics (Academic Press) ; 9
Contents Front Cover; Solution of Equations and Systems of Equations; Copyright Page; Table of Contents; Preface to the First Edition; Preface to the Second Edition; Chapter 1. Divided Differences; DIVIDED DIFFERENCES FOR DISTINCT ARGUMENTS; SYMMETRY; INTEGRAL REPRESENTATION; MEAN VALUE FORMULAS; DIVIDED DIFFERENCES WITH REPEATED ARGUMENTS; A FORMULA FOR CONFLUENT DIVIDED DIFFERENCES; NEWTON'S INTERPOLATION FORMULA; GENERAL INTERPOLATION PROBLEM; POLYNOMIAL INTERPOLATION; THE REMAINDER FOR A GENERAL INTERPOLATING FUNCTION; TRIANGULAR SCHEMES FOR COMPUTING DIVIDED DIFFERENCES
ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF (12.1)ASYMPTOTIC BEHAVIOR OF ERRORS IN THE REGULA FALSI ITERATION; A THEOREM ON ROOTS OF CERTAIN EQUATIONS; Chapter 13. n Distinct Points of Interpolation; ERROR ESTIMATES; ITERATION WITH n DISTINCT POINTS OF INTERPOLATION; DISCUSSION OF THE ROOTS OF SOME SPECIAL EQUATIONS; Chapter 14. n + 1 Coincident Points of Interpolation and Taylor Development of the Root; STATEMENT OF THE PROBLEM; A THEOREM ON INVERSE FUNCTIONS AND CONFORMAL MAPPING; THEOREM ON THE ERROR OF THE TAYLOR APPROXIMATION TO THE ROOT; DISCUSSION OF THE CONDITIONS OF THE THEOREM
Chapter 2. Inverse Interpolation. Derivatives of the Inverse Function. One Interpolation PointTHE CONCEPT OF INVERSE INTERPOLATION; DARBOUX'S THEOREM ON VALUES OF f'(x); DERIVATIVES OF THE INVERSE FUNCTION; ONE INTERPOLATION POINT; A DEVELOPMENT OF A ZERO OF f(x); Chapter 3. Method of False Position (Regula Falsi); DEFINITION OF THE REGULA FALSI; USE OF INVERSE INTERPOLATION; GEOMETRIC INTERPRETATION (FOURIER'S CONDITIONS); ITERATION WITH SUCCESSIVE ADJACENT POINTS; HORNER UNITS AND EFFICIENCY INDEX; THE ROUNDING-OFF RULE; LOCATING THE ZERO WITH THE REGULA FALSI
ERROR ESTIMATES A PRIORI AND A POSTERIORIFUNDAMENTAL EXISTENCE THEOREMS; Chapter 8. An Analog of the Newton-Raphson Method for Multiple Roots; Chapter 9. Fourier Bounds for Newton-Raphson Iteration; Chapter 10. Dandelin Bounds for Newton-Raphson Iteration; Chapter 11. Three Interpolation Points; INTERPOLATION BY LINEAR FRACTIONS; TWO COINCIDENT INTERPOLATION POINTS; ERROR ESTIMATES; USE IN ITERATION PROCEDURE; Chapter 12. Linear Difference Equations; INHOMOGENEOUS AND HOMOGENEOUS DIFFERENCE EQUATIONS; GENERAL SOLUTION OF THE HOMOGENEOUS EQUATION; LEMMA ON DIVISION OF POWER SERIES
EXAMPLES OF COMPUTATION BY THE REGULA FALSIChapter 4. Iteration; A CONVERGENCE CRITERION FOR AN ITERATION; POINTS OF ATTRACTION AND REPULSION; IMPROVING THE CONVERGENCE; Chapter 5. Further Discussion of Iterations. Multiple Zeros; ITERATIONS BY MONOTONIC ITERATING FUNCTIONS; MULTIPLE ZEROS; CONNECTION OF THE REGULA FALSI WITH THE THEORY OF ITERATION; Chapter 6. Newton-Raphson Method; THE IDEA OF THE NEWTON-RAPHSON METHOD; THE USE OF INVERSE INTERPOLATION; COMPARISON OF REGULA FALSI AND NEWTON-RAPHSON METHOD; Chapter 7. Fundamental Existence Theorems for Newton-Raphson Iteration
Bibliography Includes bibliographical references
Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
digitized 2010 HathiTrust Digital Library committed to preserve pda MiAaHDL
Print version record
Subject Equations -- Numerical solutions
Algebra.
Gleichung.
Numerische Mathematik.
Numerieke wiskunde.
Vergelijkingen (wiskunde)
Equations -- Numerical solutions.
MATHEMATICS -- Calculus.
MATHEMATICS -- Mathematical Analysis.
Form Electronic book
ISBN 1483223647 (electronic bk.)
9781483223643 (electronic bk.)