### Table 7. Free higher-order monoid.

"... In PAGE 17: ...e., the monoid a233 a87a172 whose elements are generated by the inference rules in Table7 ), and each term constant a222 a209 a208 is mapped into a basic arrow a125a125 a222 a16a126a126 a209 a59 a218 a125a125 a208 a126a126 (where a125a125 a208 a126a126... ..."

### Table 5. Performance comparison on two-dimensional FFT codes. .0

"... In PAGE 9: ... Then the FORTRAN subroutine in SGEFA performing matrix-vector multiplications was replaced with the corresonding CAL routine, MXV A. A consider- able increase in performance resulted, as shown in Table5 . However, the times reported here for the CRA Y -2 should not be taken as optimal for solving linear equations on the CRA Y -2.... In PAGE 9: ...Table5... ..."

### Table 6 Error rates for the two-dimensional elastic matching method

### Table I. Two-dimensional analysis of a semi-infinite crack in a linear elastic solid subjected to mode I loading.

### Table 1: FEM results for the two{dimensional harmonic oscillator (eq.2) at di erent re nement levels and for polynomial degree p = 1; 2; 3. l

"... In PAGE 3: ... This leads to general matrix eigenvalue problems with dimension 5 for the initial grid up to dimensions 25000 { 46000 for the nal grids. For the rst eigenvalue 0 the results are given in Table1 . The nal matrix{dimension N is restricted by the core of the used workstation (Sun SPARC station 10).... In PAGE 4: ... Thus the asymptotic convergence of the adaptive FEM with linear elements is well described by i(Nl) := ~ i(Nl) ? i;exact = Ci Nl : (3) This can be used for an extrapolation, for instance if we use eigenvalues resulting from two re nement levels by the formula i;extr: = i(Nl) ? ( i(Nl?1) ? i(Nl)) Nl?1 Nl ? Nl?1 : (4) The extrapolated values are no longer upper bound, but are one digit more accurate and thus may be used (at least) for a very reliable error esti- mation. Proposing equation 4 to the last two levels of Table1 we get... ..."

### Table 1 Functions used to generate the two-dimensional data sets

2003

"... In PAGE 6: ... Experimental results In this experiment we consider the set of eight 2-D functions used in Cherkassky, Gehring, and Mulier (1996) to compare the performance of several adaptive methods. These functions, which form a suitable test set, are described in Table1 . We use a generalized radial basis function (GRBF) allowing a different variance along each input dimension.... ..."

Cited by 2

### Table 2: Numerical results for the domain transformation technique for solving the 2D Laplace equation with prescribed surface shapes 1, 2 and 3. 3.2.2 Numerical results for the PCG method Now we want to study the number of CG-iterations needed to solve the linear system associated with the two-dimensional test problem described above. A vector 0 with

"... In PAGE 11: ... Gaussian elimination is used as the equation solver, and linear elements (triangles with three nodes) are used for the discretization. The numerical results are shown in Table2 , where nite element solutions are denoted by b apos;. Clearly, second order convergence is obtained for all test problems.... ..."

### Table 4: Higher-Order Economic Losses

"... In PAGE 5: ...oss at a single site is $3.6 million. In addition to environmental losses, other higher-order eco- nomic losses are possible in a large New Madrid earthquake. Table4 lists some of these higher-order losses and the pa- rameters that influence their levels (Eguchi et al., 1993; Wiggins, 1994).... ..."

### Table 5: Solution times (in seconds) and speedups for the restricted weakly overlap- ping algorithm on the two-dimensional problem (56) (taken from [4]).

"... In PAGE 21: ... In each case the Speedup row compares the parallel solution time (on a SGI Origin 2000 computer) with the best sequential solution time, whereas the Parallel speedup row compares the parallel solution time on D4 processors with the sequential solution time for the D4 subdomain algorithm. Table5 shows timings for the solution of the two-dimensional problem (56) using the Galerkin FE method on a square domain for which CC BC has BEBHBI elements and a uniform refinement level of C2 BP BI (hence CC C2 BP CC BI and contains BDBCBGBKBHBJBI elements). Table 6 shows timings for the solution of the three-dimensional problem A0 BD BDBCBCBCD6B4D6D9B5 B7 BE BG BD BD BD BF BH A1 D6D9 BP CU (58) using the streamline-diffusion FE method.... ..."

### Table 5: Solution times (in seconds) and speedups for the restricted weakly overlap- ping algorithm on the two-dimensional problem (56) (taken from [4]).

"... In PAGE 21: ... In each case the Speedup row compares the parallel solution time (on a SGI Origin 2000 computer) with the best sequential solution time, whereas the Parallel speedup row compares the parallel solution time on a27 processors with the sequential solution time for the a27 subdomain algorithm. Table5 shows timings for the solution of the two-dimensional problem (56) using the Galerkin FE method on a square domain for which a94 a27 has a4 a8 a6 elements and a uniform refinement level of a1 a19 a6 (hence a94 a0 a19 a94 a10 and contains a28 a47 a11a2 a4 a8 a0 a11a6 elements). Table 6 shows timings for the solution of the three-dimensional problem a79 a28 a28 a47 a47 a47 a64 a8a11a64 a0 a12a87a69 a2 a4 a28 a28 a28 a8 a11 a52 a64 a0 a19 a67 (58) using the streamline-diffusion FE method.... ..."