Numerical linear algebra and optimization, Vol.1

cover......Page cover001.djvu
title......Page img003.djvu
copyright......Page img004.djvu
preface......Page img007.djvu
table of contents......Page img011.djvu
CHAPTER 1 Introduction  ......Page img021.djvu
2.1. DEFINITIONS AND OPERATIONS ......Page img023.djvu
2.2. VECTOR SPACES ......Page img034.djvu
2.3. EIGENVALUES AND SINGULAR VALUES ......Page img042.djvu
2.4. NORMS ......Page img044.djvu
Further Reading ......Page img047.djvu
EXERCISES......Page img048.djvu
3.1. MEASURES OF CLOSENESS ......Page img053.djvu
3.2. THE EFFECTS OF FINITE PRECISION ......Page img056.djvu
3.3. CONDITION OF A MATHEMATICAL PROBLEM ......Page img063.djvu
3.4. COMPUTABLE MEASURES OF GOODNESS ......Page img065.djvu
3.5. ERROR ANALYSIS ......Page img067.djvu
3.6. CONDITION OF A LINEAR SYSTEM ......Page img070.djvu
Further Reading ......Page img078.djvu
EXERCISES......Page img079.djvu
4.1. OVERVIEW ......Page img091.djvu
4.2. TRIANGULAR LINEAR SYSTEMS ......Page img092.djvu
4.3. GAUSSIAN ELIMINATION ......Page img096.djvu
4.4. PIVOTING ......Page img105.djvu
4.5. APPLICATIONS OF ERROR ANALYSIS ......Page img112.djvu
4.6. PROPERTIES OF THE COMPUTED SOLUTION ......Page img117.djvu
4.7. USING THE INVERSE MATRIX ......Page img119.djvu
4.8. BLOCK ELIMINATION AND FACTORIZATION ......Page img124.djvu
4.9. SYMMETRIC MATRICES ......Page img126.djvu
4.10. ORTHOGONAL TRIANGULARIZATION ......Page img140.djvu
4.11. INTRODUCTION TO UPDATING ......Page img145.djvu
Further Reading ......Page img170.djvu
EXERCISES......Page img171.djvu
5.1. BEYOND NONSINGULAR SYSTEMS ......Page img181.djvu
5.2. MATRICES WITH FULL RANK ......Page img182.djvu
5.3. BACKGROUND ......Page img185.djvu
5.4. TRIANGULAR RANK-REVEALING FORM ......Page img193.djvu
5.5. THE MINIMUM-LENGTH SOLUTION ......Page img206.djvu
5.6. THE SINGULAR VALUE DECOMPOSITION ......Page img215.djvu
5.7. CONDITION OF A COMPATIBLE SYSTEM ......Page img217.djvu
5.8. ESTIMATION OF NUMERICAL RANK ......Page img219.djvu
Further Reading ......Page img225.djvu
EXERCISES......Page img226.djvu
6.1. BACKGROUND ......Page img235.djvu
6.2. FORMULATION OF A LEAST-SQUARES PROBLEM ......Page img236.djvu
6.3. PROPERTIES OF THE LEAST-SQUARES SOLUTION ......Page img238.djvu
6.4. THE NORMAL EQUATIONS ......Page img243.djvu
6.5. ORTHOGONAL TRANSFORMATION ......Page img246.djvu
6.6. THE MINIMUM-LENGTH LEAST-SQUARES SOLUTION ......Page img250.djvu
6.7. CONDITION OF THE LEAST-SQUARES PROBLEM ......Page img254.djvu
6.8. RANGE AND NULL SPACES ......Page img260.djvu
6.9. PROJECTIONS ......Page img264.djvu
Further Reading ......Page img267.djvu
EXERCISES......Page img268.djvu
7.1. INTRODUCTION ......Page img279.djvu
7.2. FORMULATING A LINEAR PROGRAM ......Page img280.djvu
7.3. LINEAR FUNCTIONS ......Page img284.djvu
7.4. LINEAR EQUALITY CONSTRAINTS ......Page img290.djvu
7.5. LINEAR INEQUALITY CONSTRAINTS ......Page img292.djvu
7.6. OPTIMALITY FOR EQUALITY CONSTRAINTS ......Page img308.djvu
7.7. OPTIMALITY FOR INEQUALITY CONSTRAINTS ......Page img313.djvu
7.8. LINEAR PROGRAMS WITH MIXED CONSTRAINTS ......Page img327.djvu
7.9. FINDING A FEASIBLE POINT ......Page img331.djvu
7.10. DUALITY ......Page img337.djvu
Further Reading ......Page img344.djvu
EXERCISES......Page img345.djvu
8.1. BACKGROUND ......Page img357.djvu
8.2. LINEAR PROGRAMS IN INEQUALITY FORM ......Page img358.djvu
8.3. DEGENERACY ......Page img368.djvu
8.4. LINEAR PROGRAMS IN STANDARD FORM ......Page img375.djvu
8.5. NON-SIMPLEX ACTIVE-SET METHODS ......Page img395.djvu
8.6. SOLVING A PHASE-1 LINEAR PROGRAM ......Page img402.djvu
8.7. COMPLEXITY OF THE SIMPLEX METHOD ......Page img415.djvu
Further Reading ......Page img418.djvu
EXERCISES......Page img419.djvu
Bibliography ......Page img429.djvu
Index ......Page img431.djvu