Nonlinear Equations - UFRJ

More documents

Recommendations

Info

Publicações Matemáticas Nonlinear Equations Gregorio Malajovich UFRJ impa 28 o Colóquio Brasileiro de Matemática
Page 3: Nonlinear Equations
Page 7: To Beatriz
Page 10 and 11: viii FOREWORD solving ( x y x) + y
Page 12 and 13: x FOREWORD The following is unknown
Page 14 and 15: xii CONTENTS 4.4 The co-area formul
Page 17 and 18: Chapter 1 Counting solutions of pol
Page 19 and 20: [SEC. 1.1: BÉZOUT’S THEOREM 3 ti
Page 21 and 22: [SEC. 1.1: BÉZOUT’S THEOREM 5 Th
Page 23 and 24: [SEC. 1.2: SHORTCOMINGS OF BÉZOUT
Page 25 and 26: [SEC. 1.3: SPARSE POLYNOMIAL SYSTEM
Page 27 and 28: [SEC. 1.4: SMALE’S 17 TH PROBLEM
Page 29 and 30: [SEC. 2.1: SYLVESTER’S RESULTANT
Page 31 and 32: [SEC. 2.2: IDEALS 15 Exercise 2.3.
Page 33 and 34: [SEC. 2.3: THE COORDINATE RING 17 o
Page 35 and 36: [SEC. 2.4: GROUP ACTION AND NORMALI
Page 41 and 42: [SEC. 2.6: THE NULLSTELLENSATZ 25 o
Page 43 and 44: [SEC. 2.6: THE NULLSTELLENSATZ 27 I
Page 45 and 46: [SEC. 2.6: THE NULLSTELLENSATZ 29 C
Page 47 and 48: [SEC. 2.7: PROJECTIVE GEOMETRY 31 D
Page 49 and 50: Chapter 3 Topology and zero countin
Page 51 and 52: [SEC. 3.1: MANIFOLDS 35 Note that i
Page 53 and 54: [SEC. 3.2: BROUWER DEGREE 37 to q.
Page 55 and 56:
[SEC. 3.2: BROUWER DEGREE 39 B a Fi
Page 57 and 58:
[SEC. 3.3: COMPLEX MANIFOLDS AND EQ
Page 59 and 60:
[SEC. 4.1: MULTILINEAR ALGEBRA OVER
Page 61 and 62:
[SEC. 4.2: COMPLEX DIFFERENTIAL FOR
Page 63 and 64:
[SEC. 4.3: KÄHLER GEOMETRY 47 then
Page 65 and 66:
[SEC. 4.4: THE CO-AREA FORMULA 49 E
Page 67 and 68:
[SEC. 4.5: PROJECTIVE SPACE 51 More
Page 69 and 70:
[SEC. 4.5: PROJECTIVE SPACE 53 The
Page 71 and 72:
Chapter 5 Reproducing kernel spaces
Page 73 and 74:
[SEC. 5.1: FEWSPACES 57 Example 5.3
Page 75 and 76:
[SEC. 5.2: METRIC STRUCTURE ON ROOT
Page 77 and 78:
[SEC. 5.3: ROOT DENSITY 61 First, w
Page 79 and 80:
[SEC. 5.4: AFFINE AND MULTI-HOMOGEN
Page 81 and 82:
[SEC. 5.5: COMPACTIFICATIONS 65 Thi
Page 83 and 84:
[SEC. 5.5: COMPACTIFICATIONS 67 4.
Page 85 and 86:
[SEC. 5.5: COMPACTIFICATIONS 69 As
Page 87 and 88:
[SEC. 5.5: COMPACTIFICATIONS 71 Exe
Page 89 and 90:
[SEC. 6.1: LEGENDRE’S TRANSFORM 7
Page 91 and 92:
[SEC. 6.2: THE MOMENTUM MAP 75 6.2
Page 93 and 94:
[SEC. 6.3: GEOMETRIC CONSIDERATIONS
Page 95 and 96:
[SEC. 6.4: CALCULUS OF POLYTOPES AN
Page 97 and 98:
[SEC. 6.4: CALCULUS OF POLYTOPES AN
Page 99 and 100:
[SEC. 7.1: THE GAMMA INVARIANT 83 T
Page 101 and 102:
[SEC. 7.1: THE GAMMA INVARIANT 85 B
Page 103 and 104:
[SEC. 7.2: THE γ-THEOREMS 87 7.2 T
Page 105 and 106:
[SEC. 7.2: THE γ-THEOREMS 89 The f
Page 107 and 108:
[SEC. 7.2: THE γ-THEOREMS 91 When
Page 109 and 110:
[SEC. 7.2: THE γ-THEOREMS 93 3−
Page 111 and 112:
[SEC. 7.2: THE γ-THEOREMS 95 Then
Page 113 and 114:
[SEC. 7.3: ESTIMATES FROM DATA AT A
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Page 123 and 124:
Chapter 8 Condition number theory 8
Page 125 and 126:
[SEC. 8.1: LINEAR EQUATIONS 109 Thi
Page 127 and 128:
[SEC. 8.3: THE CONDITION NUMBER FOR
Page 129 and 130:
[SEC. 8.4: CONDITION NUMBERS FOR HO
Page 131 and 132:
[SEC. 8.5: CONDITION NUMBERS IN GEN
Page 133 and 134:
[SEC. 8.5: CONDITION NUMBERS IN GEN
Page 135 and 136:
[SEC. 8.6: INEQUALITIES ABOUT THE C
Page 137 and 138:
Chapter 9 The pseudo-Newton operato
Page 139 and 140:
[SEC. 9.1: THE PSEUDO-INVERSE 123 i
Page 141 and 142:
[SEC. 9.2: ALPHA THEORY 125 Proof.
Page 143 and 144:
[SEC. 9.3: APPROXIMATE ZEROS 127 He
Page 145 and 146:
[SEC. 9.3: APPROXIMATE ZEROS 129 an
Page 147 and 148:
[SEC. 9.4: THE ALPHA THEOREM 131 Th
Page 149 and 150:
[SEC. 9.5: ALPHA-THEORY AND CONDITI
Page 151 and 152:
Chapter 10 Homotopy Several recent
Page 153 and 154:
[SEC. 10.1: HOMOTOPY ALGORITHM 137
Page 155 and 156:
[SEC. 10.1: HOMOTOPY ALGORITHM 139
Page 157 and 158:
[SEC. 10.2: PROOF OF THEOREM 10.5 1
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Page 165 and 166:
[SEC. 10.3: AVERAGE COMPLEXITY OF R
Page 167 and 168:
[SEC. 10.3: AVERAGE COMPLEXITY OF R
Page 169 and 170:
[SEC. 10.4: THE GEOMETRIC VERSION..
Page 171:
[SEC. 10.4: THE GEOMETRIC VERSION..
Page 174 and 175:
158 [CH. A: OPEN PROBLEMS of modern
Page 176 and 177:
160 [CH. A: OPEN PROBLEMS ζ 1 of f
Page 178 and 179:
162 [CH. A: OPEN PROBLEMS is polyno
Page 181 and 182:
Bibliography [1] P.A. Absil, J. Tru
Page 183 and 184:
BIBLIOGRAPHY 167 [27] David Cox, Jo
Page 185 and 186:
BIBLIOGRAPHY 169 [55] Gregorio Mala
Page 187:
BIBLIOGRAPHY 171 [85] Hermann Weyl,
Page 190 and 191:
174 BIBLIOGRAPHY α 0 - The constan
Page 192 and 193:
176 INDEX inner product Weyl’s, 6
show all

Nonlinear Equations - UFRJ

Create successful ePaper yourself

Delete template?

Save as template?