/P 72 0 R /Type /StructElem 703 0 obj << /Pg 63 0 R /K [ 244 0 R ] >> 1101 0 obj endobj /K [ 143 ] /S /P << 410 0 R 411 0 R 412 0 R 413 0 R 414 0 R 415 0 R 416 0 R 417 0 R 418 0 R 419 0 R 420 0 R << << /K [ 65 ] >> /Pg 57 0 R /Pg 63 0 R endobj << /K [ 113 ] /Type /StructElem >> endobj 1431 0 obj 871 0 obj (2012) A tensor decomposition approach to data compression and approximation of ND systems. /S /TD << 1466 0 obj /Type /StructElem << /K [ 95 ] << 445 0 obj /S /P /Pg 44 0 R /S /P /F8 22 0 R >> /Pg 46 0 R >> /P 354 0 R >> /Pg 49 0 R /Type /StructElem /K [ 1322 0 R ] /Pg 57 0 R endobj << /P 1119 0 R /P 1174 0 R /K [ 13 ] /K [ 73 ] /P 1315 0 R << 1099 0 R 1099 0 R 1099 0 R 1099 0 R 1099 0 R 1099 0 R 1099 0 R 1099 0 R 1101 0 R /Type /StructElem /P 317 0 R 297 0 obj /Type /StructElem /Type /StructElem /P 627 0 R << 108 0 obj >> endobj endobj endobj /K [ 269 ] /Pg 54 0 R /Pg 57 0 R ] /K [ 1241 0 R ] /P 72 0 R /Type /StructElem /S /P /P 226 0 R 1424 0 obj >> endobj /P 696 0 R /S /P 2019. /Pg 57 0 R endobj 1471 0 obj /S /TD /P 819 0 R /S /P /S /TD /Pg 49 0 R >> /P 1413 0 R endobj /Type /StructElem endobj /K [ 565 0 R ] /S /TD << << /S /P 527 0 obj /S /TD >> << /P 929 0 R >> /P 72 0 R /P 852 0 R /K [ 1107 0 R ] endobj /Pg 63 0 R /S /P >> /P 1036 0 R /K [ 2 ] /K [ 1376 0 R ] << << /Type /StructElem /K [ 73 ] /Type /StructElem /K [ 41 ] /S /TD /Pg 44 0 R endobj /P 394 0 R << /K [ 914 0 R 916 0 R 918 0 R 920 0 R 922 0 R 924 0 R 926 0 R 928 0 R ] << /Pg 54 0 R /P 1468 0 R /P 1218 0 R /K [ 121 0 R ] /Type /StructElem /Pg 49 0 R endobj endobj << /S /P /Pg 54 0 R >> endobj << /K [ 305 ] endobj /K [ 13 ] endobj /Type /StructElem 1128 0 obj /Type /StructElem /Type /StructElem 348 0 R 350 0 R 352 0 R 353 0 R 356 0 R 358 0 R 360 0 R 362 0 R 364 0 R 366 0 R 368 0 R 697 0 obj /Type /StructElem /S /TD /S /TD /S /P /K [ 24 ] (2009) Multi‐scale propagation and imaging with wave packets. << << /Pg 57 0 R /K [ 111 ] << /P 1057 0 R Numerical analysis is the area of mathematics and computer science that /Pg 44 0 R endobj /S /P /Type /StructElem /P 72 0 R endobj /S /Span /K [ 983 0 R ] /P 1178 0 R << /Type /StructElem endobj /S /TD /Type /StructElem /Pg 49 0 R >> 895 0 obj (2016) Uncertainty propagation in orbital mechanics via tensor decomposition. 249 0 obj << /S /Span 1239 0 obj /Pg 46 0 R /S /TD /P 203 0 R /K [ 49 ] /P 72 0 R endobj /S /TD /Type /StructElem << endobj /Type /StructElem 578 0 obj endobj 117 0 obj endobj /Type /StructElem >> /K [ 7 ] /P 72 0 R /P 322 0 R /K [ 747 0 R ] /S /P endobj /K [ 1131 0 R ] /Pg 49 0 R 913 0 obj endobj /Pg 57 0 R 509 0 obj /K [ 106 ] /S /TD 128 0 obj /K [ 37 ] 71 0 obj /S /P /P 72 0 R /K [ 21 ] 317 0 obj 550 0 obj /P 72 0 R /Type /StructElem /Type /StructElem endobj << << /Type /StructElem /K [ 461 0 R ] 735 0 obj /Type /StructElem /K [ 1169 0 R ] /S /TD /K [ 973 0 R ] /K [ 978 0 R 980 0 R 982 0 R 984 0 R 986 0 R 988 0 R 990 0 R 992 0 R ] endobj endobj /Pg 44 0 R << /Pg 44 0 R << 331 0 obj /Type /StructElem endobj << 1391 0 obj 1495 0 obj << /Type /StructElem >> << /P 734 0 R /P 297 0 R endobj /K [ 1 ] 1105 0 R 1107 0 R 1109 0 R 1111 0 R 1113 0 R 1115 0 R 1117 0 R 1118 0 R 1121 0 R endobj endobj /Type /StructElem /S /TD >> << >> /Type /StructElem endobj /Pg 63 0 R >> << /Type /StructElem endobj /S /P Uncertainty Quantification for Hyperbolic and Kinetic Equations, 93-125. /Pg 57 0 R /K [ 925 0 R ] /K [ 217 ] >> /Pg 49 0 R /Type /StructElem /S /P (2013) Constructive Representation of Functions in Low-Rank Tensor Formats. endobj endobj >> /K [ 222 0 R ] endobj 1301 0 R 1302 0 R 1303 0 R 1304 0 R 1305 0 R 1306 0 R 1307 0 R 1308 0 R 1309 0 R << << 496 0 obj /Type /StructElem /K [ 290 ] has led to an increasing use of realistic mathematical models in science, /Pg 44 0 R /K [ 138 ] /S /TD /Type /StructElem /P 880 0 R /K 264 /S /Figure 732 0 obj << /S /Span >> << >> endobj /S /P /Pg 34 0 R >> << >> endobj With the matrix eigenvalue problem \(Ax=\lambda x\ ,\) it is standard to transform the matrix \(A\) to a simpler form, one for which the eigenvalue problem can be solved more easily and/or cheaply. Analysis, Probability, Applications, and Computation, 27-36. /P 72 0 R endobj >> /Type /StructElem << /K [ 323 0 R 325 0 R 327 0 R 329 0 R 331 0 R 333 0 R 335 0 R 337 0 R ] /S /TD >> /Pg 57 0 R /Type /StructElem (2006) Efficient solution of Poisson’s equation with free boundary conditions. /S /TR endobj endobj /K [ 1111 0 R ] endobj /S /TD /Type /StructElem /P 1106 0 R 572 0 obj /Type /StructElem /P 72 0 R /Type /StructElem /K [ 1277 0 R ] << /P 447 0 R 762 0 obj endobj /K [ 1362 0 R ] Such problems originate generally from 380 0 obj /K [ 96 ] << /P 1208 0 R /K [ 821 0 R ] >> /S /TD /K [ 378 0 R ] 554 0 obj /Pg 63 0 R /S /P << /S /Span endobj /Pg 46 0 R /K [ 1283 0 R 1284 0 R 1285 0 R 1286 0 R 1287 0 R ] 1459 0 obj >> /CenterWindow false /P 929 0 R /P 72 0 R endobj << << /Type /StructElem /Type /StructElem It presents many techniques for the efficient numerical solution of problems in science and engineering. /K [ 112 ] /Type /StructElem 2015. 599 0 obj /Pg 57 0 R 236 0 obj /Type /StructElem /P 1454 0 R >> /K 123 /Pg 3 0 R >> << endobj /K [ 218 0 R ] /Type /StructElem /S /P >> << /S /TD /Type /StructElem /Type /StructElem /K [ 116 ] The approximating functions in \(\mathcal{F}\) are often chosen as piecewise polynomial functions which are polynomial over the elements of the mesh chosen earlier. endobj 448 0 obj /P 72 0 R /S /P /K [ 1403 0 R ] >> endobj >> /S /Span >> 867 0 obj 956 0 obj endobj /Pg 60 0 R endobj 3 0 obj /S /P 1249 0 R 1251 0 R 1253 0 R 1255 0 R 1257 0 R 1259 0 R 1261 0 R 1262 0 R 1265 0 R >> /Type /StructElem /K [ 117 ] endobj (2019) Tensor Representation of Non-linear Models Using Cross Approximations. /K [ 957 0 R ] /K [ 535 0 R ] << /S /TD 2011. /Pg 34 0 R /Type /StructElem >> /S /P /P 819 0 R endobj >> /K [ 48 ] /S /P << /Type /StructElem /Pg 63 0 R endobj /Pg 63 0 R endobj 722 0 obj /Pg 63 0 R (2013) Computing molecular correlation energies with guaranteed precision. >> (2020) Krylov subspace projection method for Sylvester tensor equation with low rank right-hand side. 266 0 obj >> >> /S /P /S /P << 866 0 R 867 0 R 868 0 R 869 0 R 870 0 R 871 0 R 872 0 R 873 0 R 874 0 R 87 0 R 853 0 R << << >> /Type /StructElem /Type /StructElem endobj There is a fundamental concern with error, its size, and its analytic form. endobj endobj /P 458 0 R /S /P /Type /StructElem /P 707 0 R /S /TD << endobj 559 0 obj /Pg 57 0 R << endobj /P 306 0 R endobj endobj /P 365 0 R 1277 0 obj 1075 0 obj 443 0 obj /P 940 0 R << /Pg 44 0 R /Pg 3 0 R 462 0 obj endobj >> /Pg 57 0 R << 1025 0 obj /Type /StructElem 846 0 obj >> /P 193 0 R /Type /StructElem /Pg 57 0 R (2012) Computing many-body wave functions with guaranteed precision: The first-order Møller-Plesset wave function for the ground state of helium atom. /S /TD /Type /StructElem /Type /StructElem 1056 0 obj /S /P /Pg 46 0 R 419 0 obj /Pg 57 0 R /P 1383 0 R endobj /Pg 44 0 R /S /TD /P 1167 0 R endobj /Pg 57 0 R 268 0 obj (2012) Stochastic Boundary Methods of Fundamental Solutions for solving PDEs. /S /TD endobj /Pg 46 0 R /S /TD /K [ 172 173 174 175 176 177 178 179 180 ] >> << /Type /StructElem << >> endobj /S /P /K [ 1157 0 R ] (2010) Digital Predistortion for Power Amplifiers Using Separable Functions. /Type /StructElem /Type /StructElem /Type /StructElem /Pg 57 0 R /P 1087 0 R >> /Type /StructElem << /P 723 0 R /K [ 73 0 R 76 0 R 77 0 R 78 0 R 79 0 R 80 0 R 82 0 R 84 0 R 85 0 R 86 0 R 87 0 R 89 0 R /Type /StructElem /Type /StructElem /S /P << << endobj /Pg 57 0 R << /K [ 291 ] 1496 0 obj << >> /S /Span /K [ 1149 0 R ] << /Pg 63 0 R >> << /Pg 49 0 R /P 72 0 R endobj /P 72 0 R 994 0 obj (2015) Using Nested Contractions and a Hierarchical Tensor Format To Compute Vibrational Spectra of Molecules with Seven Atoms. << /P 386 0 R 99 0 obj /Type /StructElem /S /P /K [ 24 ] endobj << >> 602 0 obj >> >> (2017) Orbit uncertainty propagation and sensitivity analysis with separated representations. /Pg 44 0 R 766 0 obj << /Type /StructElem << /K [ 94 ] >> /K 121 1039 0 obj 231 0 obj endobj endobj 243 0 obj (2016) Sequential alternating least squares for solving high dimensional linear Hamilton-Jacobi-Bellman equation. 995 0 R 997 0 R 999 0 R 1001 0 R 1003 0 R 1005 0 R 1007 0 R 1008 0 R 1011 0 R 1013 0 R 453 0 obj /Pg 44 0 R << /Type /StructElem /P 945 0 R (2008) A linear-scaling spectral-element method for computing electrostatic potentials. /Pg 44 0 R 1260 0 obj /Type /StructElem << /K [ 33 ] /Type /StructElem << /Pg 44 0 R >> /S /TD /Type /StructElem /S /TD /S /TD Activities include organising international conferences and a Numerical Analysis and Scientific Computing seminar series, writing textbooks and research monographs, membership of editorial boards of international journals and book series, and contributing software to the NAG and LAPACK libraries and MATLAB.