| ACKNOWLEDGEMENTS | 第1-6页 |
| ABSTRACT | 第6-7页 |
| 摘要 | 第7-8页 |
| CONTENTS | 第8-12页 |
| LIST OF FIGURES | 第12-13页 |
| LIST OF TABLES | 第13-14页 |
| CHAPTER 1 INTRODUCTION | 第14-23页 |
| ·LITERATURE REVIEWS | 第18-21页 |
| ·OUTLINES OF THE DISSERTATION | 第21-23页 |
| CHAPTER 2 MATHEMATICAL PRELIMINARY CONCEPTS | 第23-33页 |
| ·INTRODUCTION TO POLYNOMIAL ROOTS AND THEIR PERTURBATIONS | 第23-24页 |
| ·REVIEWS OF SOME MATHEMATICAL TERMS | 第24-26页 |
| ·SOURCES OF NONLINEAR EQUATIONS | 第26-28页 |
| ·FORMULATING PROBLEMS AND STEPS IN MATHEMATICAL METHODS | 第28-31页 |
| ·CONSTRUCTION OF ITERATIVE METHODS | 第30-31页 |
| ·THE PERFORMANCE ANALYSES OF ITERATIVE ALGORITHMS | 第31-32页 |
| ·COMPLEXITY AND GENERIC CHOICE OF AN ALGORITHM | 第32-33页 |
| CHAPTER 3 REVIEWS OF NUMERICAL ERRORS AND THEIRSOURCES | 第33-46页 |
| ·TYPES AND SOURCES OF ERRORS | 第33-39页 |
| ·BASIC INTRODUCTION OF ERRORS | 第33-35页 |
| ·ROUND OFF ERRORS | 第35页 |
| ·TRUNCATION ERRORS (IN FUNCTION APPROXIMATION) | 第35-37页 |
| ·ERRORS IN FUNCTION EVALUATIONS (COMPUTATIONS OF FUNCTIONS) | 第37页 |
| ·ARITHMETIC ERRORS | 第37-38页 |
| ·ERRORS DUE TO NUMERICAL ALGORITHM FOR A GIVEN NUMERICAL METHOD | 第38-39页 |
| ·ERRORS, STABILITY AND CONDITIONING OF A PROBLEM | 第39-45页 |
| ·REVIEWS OF FREQUENTLY USED VECTOR NORMS | 第39-40页 |
| ·CONDITIONING OF MATHEMATICAL PROBLEM | 第40-42页 |
| ·CONDITIONING OF ROOT FINDING FOR REAL VALUED SCALAR EQUATIONS | 第42-45页 |
| ·ERRORS IN FLOATING POINT OPERATIONS | 第45-46页 |
| CHAPTER 4 THE CONCEPT OF MODELING AND ERRORS | 第46-58页 |
| ·INTRODUCTION TO MODELING | 第46-48页 |
| ·MODELING-DEFINITION | 第46-48页 |
| ·THINGS OF INTERESTS IN MODELING | 第48页 |
| ·Interpolation models and iterative methods | 第48-51页 |
| ·NEWTON'S FORWARD FINITE DIFFERENCE INTERPOLATION | 第49页 |
| ·LAGRANGE'S INTERPOLATION | 第49-50页 |
| ·GENERALIZED NEWTON'S FORMULA(NEWTON'S DIVIDED DIFFERENCE FORMULA,NDDF) | 第50页 |
| ·LAGRANGE'S INVERSE-INTERPOLATION | 第50-51页 |
| ·ERRORS IN THE INTERPOLATION MODELS | 第51页 |
| ·STABILITY OF NUMERICAL METHODS IN MODEL SOLUTIONS | 第51-54页 |
| ·THE TWO MAIN STOPPING CRITERIA FOR ITERATIVE METHODS | 第52页 |
| ·A PRIORI AND A POSTERIORI ERRORS ANALYSES | 第52-53页 |
| ·MODELING AND MEASURES TO REDUCE COMPUTATIONAL ERRORS | 第53-54页 |
| ·EXAMPLE ON SOURCE OF NONLINEAR(MODELS)EQUATIONS | 第54-58页 |
| ·STABILITY ANALYSIS OF NUMERICAL ODE AS A SOURCE OF NONLINEAR EQUATIONS | 第55-58页 |
| CHAPTER 5 SCALAR POLYNOMIALS AND ILL-CONDITIONING | 第58-107页 |
| ·INTRODUCTION TO THE SOLUTION OF SCALAR EQUATIONS | 第58页 |
| ·BASIC CONCEPTS ON ROOTS OF POLYNOMIAL EQUATIONS | 第58-60页 |
| ·TESTS FOR EXISTENCE OF ROOTS OR ZEROS AND ROOTLOCATIONS | 第60-63页 |
| ·LOCATION PRINCIPLE FOR ROOT OF A POLYNOMIAL AND ITS DERIVATIVE | 第61页 |
| ·BOUND OF REAL ROOTS | 第61-63页 |
| ·GRAPHICAL-METHOD[GEOMETRIC APPROACH] | 第63-64页 |
| ·FURTHER DISCUSSIONS ON POLYNOMIAL ROOTS | 第64-66页 |
| ·CENTER OF MASS AND THE CONVEX HULL OF ROOTS | 第65-66页 |
| ·ROOTS OF A POLYNOMIAL AND ITS DERIVATIVES(BOUNDSAND LOCALIZATIONS) | 第66-80页 |
| ·LOCALIZATION OF THE(COMPLEX)ROOTS OF THE DERIVATIVES | 第66-67页 |
| ·LEHMER'S METHOD | 第67页 |
| ·COMMON ROOTS OF TWO POLYNOMIALS | 第67-68页 |
| ·SEPARATION OF ROOTS | 第68-69页 |
| ·THE RELATIONS OF COEFFICIENTS AND ROOTS AND DEGREE OF A POLYNOMIAL | 第69-74页 |
| ·FACTORING A POLYNOMIAL(REMAINDER THEOREM AND FACTOR THEOREM) | 第74-75页 |
| ·SOL VING CUBIC AND QUARTIC POLYNOMIALS, CARDANO'S FORMULA | 第75-80页 |
| ·THE HORNER'S METHOD AND POLYNOMIAL REPRESENTATIONS | 第80-85页 |
| ·HORNER'S NESTED MULTIPLICATION ALGORITHM FOR POLYNOMIALS | 第81-82页 |
| ·SYNTHETIC DIVISION ALGORITHM(SYNDV) | 第82-85页 |
| ·PERTURBATION METHODS FOR SOLVING ROOTS OF ALGEBRAIC EQUATIONS | 第85-87页 |
| ·SOFTWARE ROOT SOLVERS(SRS) | 第87-90页 |
| ·MATLAB ROOT SOLVERS(MRS) | 第87-88页 |
| ·MAPLE ROOT FINDERS | 第88-89页 |
| ·MATHEMATICA ROOT SOLVERS | 第89-90页 |
| ·THE BERNSTEIN POLYNOMIALS AND APPLICATIONS | 第90-92页 |
| ·SENSITIVITY OF A POLYNOMIAL ROOT TO THE PERTURBATION IN ITS COEFFICIENTS(MAIN FOCUS OF THE THESIS) | 第92-107页 |
| CHAPTER 6 ITERATIVE ALGORITHMS FOR SCALAR NONLINEAREQUATIONS | 第107-130页 |
| ·INDUCTION | 第107-121页 |
| ·SOME EXISTING ITERATIVE METHODS | 第107-108页 |
| ·BISECTION METHOD(BM) | 第108-109页 |
| ·REGULA FALSI METHOD(RFM) | 第109-111页 |
| ·NEWTON'S METHOD | 第111-113页 |
| ·FIXED-POINT ITERATION METHOD(FPM) | 第113-115页 |
| ·THE SECANT METHOD(SM) | 第115-117页 |
| ·STEFFENSEN'S METHOD AND OTHER DERIVATIVE FREE METHODS | 第117-118页 |
| ·ITERATIVE METHODS USING QUADRATIC INTERPOLATION | 第118-121页 |
| ·METHODS WITH HIGHER ORDER DERIVATIVES | 第121-122页 |
| ·CLASSICAL METHODS | 第122-123页 |
| ·Algorithms using perturbation theory and Taylor's series | 第123-124页 |
| ·ALGORITHMS USING TAYLOR'S APPROXIMATION (EXTENSIONS OF NEWTON'S FORMULA) | 第124页 |
| ·ITERATIVE METHOD FOR MULTIPLE ROOTS | 第124-126页 |
| ·GENERALIZED NEWTON'S METHOD(MODIFIED NEWTON'S METHOD) | 第125-126页 |
| ·VARIATIONAL METHODS FOR MULTIPLE ROOTS | 第126页 |
| ·SIMULTANEOUS ROOT FINDERS | 第126-128页 |
| ·RATE AND ORDER OF CONVERGENCE | 第128-130页 |
| CHAPTER 7 FURTHER ANALYSES AND SUGGESTIONS OF NEWITERATIVE METHODS | 第130-192页 |
| ·NEW ITERATIVE METHODS FOR SIMPLE ROOTS USING FUNCTION CONSTRUCTION | 第130-132页 |
| ·ITERATIVE ALGORITHMS USING DERIVATIVE ESTIMATIONS IN TAYLOR'S THIRD ORDER INTERPOLATION | 第132-141页 |
| ·A STATEMENT OF THE HIGHER DERIVATIVE ESTIMATIONS | 第133页 |
| ·ITERATIVE METHODS APPLYING DERIVATIVE ESTIMATIONS | 第133-138页 |
| ·CONVERGENCE ANALYSIS | 第138-139页 |
| ·TEST EQUATIONS AND NUMERICAL RESULTS | 第139-141页 |
| ·SUMMARY | 第141页 |
| ·CONSTRUCTION OF ITERATIVE METHODS FOR MULTIPLEROOTS | 第141-144页 |
| ·NEWTON METHOD FOR MULTIPLE ROOTS AND NEWTON-CORRECTION | 第142-144页 |
| ·CONSTRUCTION OF THIRD ORDER METHODS FOR MULTIPLE ROOTS | 第144页 |
| ·CONVERGENCE ANALYSIS | 第144-145页 |
| ·TEST EQUATIONS AND NUMERICAL RESULTS | 第145-146页 |
| ·SUMMARY(CONCLUDING REMARKS) | 第146-147页 |
| ·APPLICATION OF ROOT FINDING | 第147-157页 |
| ·APPLICATION OF ROOT FINDING IN THE STABILITY ANALYSIS OF NUMERICAL ODE(FE,EB,RK2,RK3,RK4) | 第147-152页 |
| ·APPLICATION IN MODEL SOLUTIONS | 第152-157页 |
| ·PERTURBATION EFFECT OF A POLYNOMIAL ON THE RESULTSOF AN ITERATIVE ALGORITHM | 第157-158页 |
| ·C++ IMPLEMENTATIONS | 第158-187页 |
| ·NUMERICAL RESULTS | 第187-188页 |
| ·RESEARCH SUMMARY | 第188-192页 |
| REFERENCES | 第192-198页 |
