Front Cover; AnalyticComputational Complexity; Copyright Page; Table of Contents; LIST OF INVITED AUTHORS; PREFACE; CHAPTER 1.INTRODUCTION; CHAPTER 2.SOME REMARKS ON PROOF TECHNIQUES IN ANALYTIC COMPLEXITY; References; CHAPTER 3.STRICT LÖWER AND UPPER BOUNDS ON ITERATIVE COMPUTATIONAL COMPLEXITY; 1. INTRODUCTION; 2. BASIC CONCEPTS; 3. BOUNDS ON THE ERROR COEFFICIENT FUNCTION; 4. THE VARIABLE ERROR COEFFICIENT MODEL; 5. BOUNDS ON THE COMPLEXITY INDEX; 6. SUMMARY AND EXTENS IONS TO THE MODEL; ACKNOWLEDCMNT; REFERENCES

CHAPTER 4.THE COMPLEXITY OF OBTAINING STARTING POINTS FOR SOLVING OPERATOR EQUATIONS BY NEWTON'S METHOD1. INTRODUCTION; 2. METHODOLOGY AND A USEFUL LEMMA FOR PROVING LOWER BOUNDS; 3. SOME RESULTS ON REAL VALUED FUNCTIONS OF ONE VARIABLE; 4. A PROCEDURE TO OBTAIN GOOD STARTING POINTS FOR NEWTON'SMETHOD; 5. SUMMARY AND CONCLUSIONS; ACKNOWLEDGMENTS; REFERENCES; CHAPTER 5.A CLASS OF OPTIMAL-ORDER ZERO-FINDING METHODS USING DERIVATIVE EVALUATIONS; 1. INTRODUCTION; 2. MOTIVATION; 3. A SIXTH-ORDER METHOD; 4. METHODS OF ORDER 2v; 5. RELATED NONLINEAR RUNGE-KUTTA METHODS; 6. SOME NUMERICAL RESULTS

CHAPTER 8.THE USE OF INTEGRALS IN THE SOLUTION OF NONLINEAR EQUATIONS IN N DIMENSIONS1. INTRODUCTION; 2. AN INTERPOLATORY-INTEGRAL ITERATION I_ 1,s; 3. ORDER OF THE INTEGRAL INFORMATION; 4. COMPLEXITY INDEX; 5. INTEGRAL INFORMATION WITH KERNELS; ACKNOWLEDGMENT; 6. REFERENCES; Chapter 9. Complexity and Differential Equations; 1. INTRODUCTION; 2. GENERALIZED INTERPOLATION PROBLEMS; 3. SPARSE LINEAR SYSTEMS; 4. SPARSE NONLINEAR SYSTEMS; REFERENCES; CHAPTER 10.MULTIPLE-PRECISION ZERO-FINDING METHODS AND THE COMPLEXITY OF ELEMENTARY FUNCTION EVALUATION; 1. INTRODUCTION