TABLE OF CONTENTS ACKNOWLEDGEMENTS.................................... ABSTRACT.............................................. CHAPTERS: 1 INTRODUCTION.................................. 2 INDEXED EQUATIONS............................. 2.1 Conventions Used in Describing Indexed Equations ............................... 2.2 Function-Variable Incidence Matrices.... 2.3 Index Display Matrices.................. 2.4 Index Imbedding......................... 2.5 Output Set Assignments ................. 2.6 Acceleration of Variables.............. 3 SOLUTION PROCEDURES FOR INDEX EQUATION SETS... 3.1 Definitions............................. 3.2 An Example Problem...................... 3.3 Output Sets and Decision Variables...... 3.4 Index Imbedding ........................ 3.5 Decoupling ............................. 3.6 Blocking Factors............................... 4 ALGORITHMS FOR DERIVING SOLUTION PROCEDURES FOR SETS OF INDEXED EQUATIONS ............................... 4.1 Decoupling.................................. 4.2 Index Output Set Assignments .................. iii vi