Solution of Equations in Euclidean and Banach Spaces (Pure & Applied Mathematics). THIRD EDITION

✍ Scribed by A. M. Ostrowski

• Publisher: Academic Press
• Year: 1973
• Tongue: English
• Leaves: 433
• Edition: 3d ed
• Category: Library

✦ Table of Contents

SOLUTION OF EQUATIONS IN EUCLIDEAN AND BANACH SPACES
Copyright Page
Contents
Preface to the Third Edition
List of Notations and Abbreviations
CHAPTER 1A. DIVIDED DIFFERENCES
CHAPTER 1B. CONFLUENT CASE. INTERPOLATION
CHAPTER 2. INVERSE INTERPOLATION . DERIVATIVES OF THE INVERSE FUNCTION . ONE INTERPOLATION POINT
CHAPTER 3. METHOD OF FALSE POSITION (REGULA FALSI)
CHAPTER 4. ITERATION
CHAPTER 5. FURTHER DISCUSSION OF ITERATIONS. MULTIPLE ZEROS
CHAPTER 6. THE NEWTON–RAPHSON METHOD
CHAPTER 7. FUNDAMENTAL EXISTENCE THEOREMS IN THE N EWTON–RAPHSON ITERATI ON
CHAPTER 8. AN ANALOG OF THE NEWTON–RAPHSON METHOD FOR MULTIPLE ROOTS
CHAPTER 9. FOURIER BOUNDS FOR THE NEWTON–RAPHSON ITERATION
CHAPTER 10. DANDELIN BOUNDS FOR THE NEWTON–RAPHSON ITERATION
CHAPTER 11. THREE INTERPOLATION POINTS
CHAPTER 12. LINEAR DIFFERENCE EQUATIONS
CHAPTER 13. n DISTINCT POINTS OF INTERPOLATION
CHAPTER 14. n+l COINCIDENT INTERPOLATION POINTS AND TAYLOR DEVELOPMENT OF THE ROOT
CHAPTER 15. THE SQUARE ROOT ITERATION
CHAPTER 16. FURTHER DISCUSSION OF SQUARE ROOT ITERATION
CHAPTER 17. A GENERAL THEOREM ON ZEROS OF INTERPOLATING POLYNOMIALS
CHAPTER 18. APPROXIMATION OF EQUATIONS BY ALGEBRAIC EQUATIONS OF A GIVEN DEGREE. ASYMPTOTIC ERRORS FOR SIMPLE ROOTS
CHAPTER 19. NORMS OF VECTORS AND MATRICES
CHAPTER 20. TWO THEOREMS ON CONVERGENCE OF PRODUCTS OF MATRICES.
CHAPTER 21. A THEOREM ON DIVERGENCE OF PRODUCTS OF MATRICES
CHAPTER 22. CHARACTERIZATION OF POINTS OF ATTRACTION AND REPULSION FOR ITERATIONS WITH SEVERAL VARIABLES
CHAPTER 23. EUCLIDEAN NORMS
CHAPTER 24. MINKOWSKI NORMS, Δp(A), Δp,p'(A)
CHAPTER 25. METHOD OF STEEPEST DESCENT. CONVERGENCE OF THE PROCEDURE
CHAPTER 26. METHOD OF STEEPEST DESCENT. WEAKLY LINEAR CONVERGENCE OF THE ζ μ
CHAPTER 27. METHOD OF STEEPEST DESCENT. LINEAR CONVERGENCE OF THE ζ μ
CHAPTER 28. CONVERGENT PROCEDURES FOR POLYNOMIAL EQUATIONS
CHAPTER 29. J-TEST AND J-ROUTINE
CHAPTER 30. q-ACCELERATION. THE PRACTICE OF THE PROCEDURE
CHAPTER 31. NORMED LINEAR SPACES
CHAPTER 32. METRIC SPACES
CHAPTER 33. OPERATORS IN NORMED LINEAR SPACES
CHAPTER 34. INVERSE OPERATORS
CHAPTER 35. OPERATORS MAPPING A LINEAR INTERVAL
CHAPTER 36. THE DIRECTIONAL DERIVATIVES AND GRADIENTS OF OPERATORS
CHAPTER 37. CENTRAL EXISTENCE THEOREM
CHAPTER 38. NEWTON–RAPHSON ITERATION IN BANACH SPACES. STATEMENT OF THE THEOREMS
CHAPTER 39. PROOF OF THEOREMS 38.1–38.3
CHAPTER 40. COMPLEMENTS TO THE NEWTON-RAPHSON METHOD
CHAPTER 41. CENTRAL EXISTENCE THEOREM FOR FINITE SYSTEMS OF EQUATIONS
CHAPTER 42. NEWTON–RAPHSON ITERATION FOR FINITE SYSTEMS OF EQUATIONS
APPENDICES
Bibliographical Notes
Index