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From Oil Fields to Hilbert Schemes |
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1 | (54) |
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A Problem Arising in Industrial Mathematics |
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5 | (5) |
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10 | (8) |
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The Eigenvalue Method for Solving Polynomial Systems |
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18 | (4) |
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Approximate Vanishing Ideals |
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22 | (9) |
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31 | (9) |
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Border Basis and Grobner Basis Schemes |
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40 | (15) |
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53 | (2) |
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Numerical Decomposition of the Rank-Deficiency Set of a Matrix of Multivariate Polynomials |
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55 | (24) |
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59 | (4) |
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Genericity and Randomness |
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59 | (1) |
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The Numerical Irreducible Decomposition |
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60 | (2) |
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62 | (1) |
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Random Coordinate Patches on Grassmannians |
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63 | (2) |
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Finding Rank-Dropping Sets |
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65 | (2) |
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67 | (2) |
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69 | (2) |
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69 | (1) |
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Degeneracy Sets of the Differential of a Map |
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70 | (1) |
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70 | (1) |
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Implementation Details and Computational Results |
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71 | (1) |
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Singular Set for a Matrix |
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71 | (1) |
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Singular Set for a Hessian Matrix |
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71 | (1) |
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Singular Solutions for a Polynomial System |
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72 | (1) |
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The Singular Set of the Reduction of an Algebraic Set |
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72 | (7) |
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Equations Defining an Algebraic Set |
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73 | (2) |
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Computing the Singular Set of the Reduction of an Algebraic Set |
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75 | (1) |
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75 | (4) |
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Towards Geometric Completion of Differential Systems by Points |
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79 | (20) |
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80 | (2) |
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80 | (1) |
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Exact Differential Elimination Algorithms |
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81 | (1) |
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82 | (1) |
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82 | (1) |
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83 | (3) |
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84 | (1) |
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85 | (1) |
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Geometric Lifting and Singular Components |
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86 | (2) |
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Determination of Singular Components of an ODE using Numerical Jet Geometry |
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88 | (2) |
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Determination of Singular Components of a PDE System |
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90 | (4) |
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94 | (5) |
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95 | (4) |
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Geometric Involutive Bases and Applications to Approximate Commutative Algebra |
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99 | (26) |
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Jet Spaces and Geometric Involutive Bases |
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102 | (5) |
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Jet Geometry and Jet Space |
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102 | (1) |
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Prolongation and Projection |
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103 | (2) |
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105 | (1) |
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Indices and Cartan Characters |
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105 | (1) |
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The Cartan-Kuranishi Prolongation Theorem |
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106 | (1) |
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Geometric Projected Involutive Bases and Nearby Systems |
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107 | (5) |
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Geometric Projected Involutive Bases |
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107 | (1) |
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Approximately Involutive Systems |
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108 | (2) |
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Nearby Systems: Structure and Convergence |
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110 | (2) |
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112 | (2) |
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Definition and Key Properties |
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112 | (1) |
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Connection with Involutive Systems |
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112 | (1) |
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113 | (1) |
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114 | (5) |
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114 | (1) |
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Grobner Bases for Polynomial Systems |
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115 | (4) |
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119 | (6) |
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4.5.1 The SVD, ε-Rank, and τ-Rank |
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119 | (1) |
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120 | (1) |
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121 | (2) |
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123 | (2) |
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Regularization and Matrix Computation in Numerical Polynomial Algebra |
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125 | (38) |
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Notation and preliminaries |
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127 | (7) |
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127 | (1) |
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Numerical rank and kernel |
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128 | (3) |
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The linear and nonlinear least squares problems |
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131 | (3) |
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Formulation of the approximate solution |
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134 | (8) |
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The ill-posed problem and the pejorative manifold |
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134 | (4) |
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The three-strikes principle for removing ill-posedness |
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138 | (4) |
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Matrix computation arising in polynomial algebra |
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142 | (8) |
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142 | (2) |
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The multiplicity structure |
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144 | (2) |
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146 | (1) |
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Approximate irreducible factorization |
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147 | (3) |
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A subspace strategy for efficient matrix computations |
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150 | (5) |
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The closedness subspace for multiplicity matrices |
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150 | (3) |
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The fewnomial subspace strategy for multivariate polynomials |
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153 | (2) |
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155 | (8) |
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158 | (5) |
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Ideal Interpolation: Translations to and from Algebraic Geometry |
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163 | (30) |
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163 | (7) |
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164 | (1) |
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165 | (2) |
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167 | (1) |
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168 | (2) |
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Hermite Projectors and Their Relatives |
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170 | (9) |
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Perturbations of ideal projectors |
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170 | (1) |
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Lagrange and curvilinear projectors |
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171 | (2) |
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Limits of Lagrange and curvilinear projectors |
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173 | (3) |
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176 | (1) |
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Existence of non-Hermite projectors |
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177 | (1) |
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Description of non-Hermite projectors |
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178 | (1) |
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Projectors in three variables |
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179 | (6) |
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Nested Ideal Interpolation |
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180 | (1) |
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181 | (1) |
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A conjecture of Tomas Sauer |
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182 | (1) |
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183 | (1) |
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183 | (2) |
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185 | (2) |
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187 | (6) |
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190 | (3) |
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An Introduction to Regression and Errors in Variables from an Algebraic Viewpoint |
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193 | (12) |
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Regression and the X -matrix |
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193 | (3) |
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Orthogonal polynomials and the residual space |
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196 | (2) |
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The fitted function and its variance |
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198 | (1) |
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``Errors in variables'' analysis of polynomial models |
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199 | (2) |
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201 | (1) |
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202 | (3) |
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202 | (3) |
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ApCoA = Embedding Commutative Algebra into Analysis |
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205 | (14) |
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205 | (1) |
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Approximate Commutative Algebra |
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206 | (1) |
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207 | (1) |
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Valid Results; Validity Checking of Results |
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208 | (1) |
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209 | (1) |
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Analytic View of Data → Result Mappings |
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210 | (1) |
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211 | (2) |
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213 | (1) |
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214 | (1) |
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215 | (2) |
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217 | (2) |
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217 | (2) |
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Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares |
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219 | |
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225 | |
Lisainfo e-raamatute kohta