COMPUTATIONAL MATHEMATICS REVIEW

By G. JOLAN

CONTENTS CHAPTER 1 - GRAPH THEORY AND NETWORK ANALYSIS 11 DEFINITIONS AND EXAMPLES 12 SPANNING TREES UNDIRECTED SPANNING TREES DIRECTED SPANNING TREES 13 MINIMAL COST NETWORKS UNDIRECTED GRAPHS DIRECTED GRAPHS 14 CRITICAL PATH ALGORITHM 15 MAXIMAL FLOW PROBLEMS PROBLEM DESCRIPTION MAIN RESULTS AND ALGORITHM EXAMPLES 16 MAXIMUM MATCHING PROBLEMS DEFINITIONS AND PROBLEM DESCRIPTION MATCHING ALGORITHM 17 OTHER PROBLEMS OF GRAPH THEORY GRAPH COLORING PROBLEM SHORTEST PATHS PROBLEM TRAVELING SALESMAN PROBLEM CHAPTER 2 - LINEAR PROGRAMMING 21 TWO-VARIABLE PROBLEMS 22 GEOMETRY OF LINEAR PROGRAMMING 23 SIMPLEX ALGORITHM FOR THE STANDARD MAXIMUM PROBLEM THE SIMPLEX ALGORITHM SPECIAL BEHAVIOR TABLEAU METHOD 24 DUALITY AND THE STANDARD MINIMUM PROBLEM CHAPTER 3 - FURTHER TOPICS IN LINEAR PROGRAMMING 31 NON-STANDARD PROBLEMS 32 TRANSPORTATION PROBLEM 33 SENSITIVITY ANALYSIS DISCUSSION OF THE PROBLEM MATRIX-GEOMETRIC VIEW OF THE SIMPLEX METHOD DETERMINING SENSITIVITY OF PARAMETERS CONTENTS CHAPTER 4 - MARKOV CHAINS 41 DEFINITIONS AND EXAMPLES SIMULATION 42 SHORT-RUN DISTRIBUTIONS 43 FIRST PASSAGE TIMES 44 CLASSIFICATION OF STATES 45 LIMITING PROBABILITIES MAIN RESULTS LONG-RUN DISCOUNTED COST 46 ABSORPTION PROBABILITIES CHAPTER 5 - CONTINUOUS TIME PROCESSES 51 POISSON PROCESSES DEFINITIONS AND MAIN RESULTS 52 BIRTH AND DEATH PROCESSES PRELIMINARIES KOLMOGOROV EQUATIONS 53 RENEWAL PROCESSES INTRODUCTION SHORT-RUN DISTRIBUTIONS LONG-RUN RESULTS RENEWAL REWARD PROCESSES 54 QUEUEING THEORY SIMPLE POISSONIAN QUEUES M/G/1 QUEUE G/M/1 QUEUE 55 BROWNIAN MOTION RELATION TO RANDOM WALKS DEFINITION AND PROPERTIES OF STANDARD BROWNIAN MOTION BROWNIAN MOTION WITH DRIFT CHAPTER 6 - DYNAMIC PROGRAMMING 61 THE MARKOVIAN DECISION MODEL DETERMINISTIC DYNAMIC PROGRAMMING STOCHASTIC DYNAMIC PROGRAMMING: THE FINITE HORIZON PROBLEM 62 THE FINITE HORIZON PROBLEM DYNAMIC PROGRAMMING ALGORITHM, STOCHASTIC CASE 63 THE DISCOUNTED REWARD PROBLEM METHOD OF SUCCESSIVE APPROXIMATIONS 64 POLICY IMPROVEMENT MAIN THEOREM AND POLICY IMPROVEMENT ALGORITHM CONTENTS EXAMPLES 65 OPTIMAL STOPPING OF A MARKOV CHAIN DYNAMIC PROGRAMMING APPROACH LINEAR PROGRAMMING APPROACH 66 EXTENDED APPLICATIONS AMERICAN OPTION PROBLEM INVENTORY PROBLEM CONCLUSION