### Table 2. Maximum error and order of convergence for nonlinear solutions with Dirichlet boundary conditions on refined grids.

"... In PAGE 19: ... First we numerically solve the Laplace equation with these exact solu- tions with Dirichlet boundary conditions everywhere. The errors and orders of convergence on our sequence of refined grids is presented in Table2 . The errors and orders of convergence of the same problems, now however with Dirichlet boundary conditions only at the right side of the solution square and with Neumann boundary conditions on the remaining three sides, is shown in Table 3.... ..."

### Table 2. Number of GMRES iterations for the related system (6) using an ILU(0) or AMG splitting of the (1,1) block and struc- tured probing to approximate the Schur complement, for various levels of h-refinement on a single non-linear iteration in the metal deformation problem. Dashes indicate insufficient memory to run that particular combination.

2006

"... In PAGE 16: ... For each of these problems, we use structured probing with the prime divisor, balanced and greedy colorings and an ILU(0) factorization of the approximate Schur complement. Table2 shows the number of GMRES iterations necessary to solve the related system (6) to a tolerance... In PAGE 17: ... If the splitting is poor, a better approximation to the Schur complement is unlikely to yield a significant improvement in convergence. We see this effect in Table2 . The difference between the prime divisor coloring, which uses more vectors than the balanced or greedy colorings for a given stencil, is most pronounced when we use the exact splitting, F = A.... ..."

### Table 1. Camera position error relative to ground truth. Non-linear minimization of the reprojection errors for only twelve fiducial markers (three targets) provides centimeter level camera position accuracy.

"... In PAGE 5: ... One often proposed method for obtaining a more accurate camera pose is to compute the average of the solutions obtained from several individual targets. This does provide an improvement over the single target solu- tion (Figure 5 and Table1 ), but further reductions are pos- sible through simultaneous estimation. Initialization of the nonlinear iteration can be performed by an algorithm such as POSIT [7], and then followed with non-linear optimiza- tion to minimize the reprojection error.... In PAGE 5: ... The path computed by non-linear refine- ment of the POSIT pose estimate is shown in Figure 6. As shown in Table1 , our camera tracking system yields a ten-... ..."

### Table 1. Camera position error relative to ground truth. Non-linear minimization of the reprojection errors for only twelve fiducial markers (three targets) provides centimeter level camera position accuracy.

"... In PAGE 5: ... One often proposed method for obtaining a more accurate camera pose is to compute the average of the solutions obtained from several individual targets. This does provide an improvement over the single target solu- tion (Figure 5 and Table1 ), but further reductions are pos- sible through simultaneous estimation. Initialization of the nonlinear iteration can be performed by an algorithm such as POSIT [7], and then followed with non-linear optimiza- tion to minimize the reprojection error.... In PAGE 5: ... The path computed by non-linear refine- ment of the POSIT pose estimate is shown in Figure 6. As shown in Table1 , our camera tracking system yields a ten-... ..."

### Table 2. The errors and orders of convergence of the same problems, now however with Dirichlet boundary conditions only at the right side of the solution square and with Neumann boundary conditions on the remaining three sides, is shown in Table 3. Both tables confirm the second order convergence rate of our method.

"... In PAGE 19: ... Table2 . Maximum error and order of convergence for nonlinear solutions with Dirichlet boundary conditions on refined grids.... ..."

### Table 1: Comparing results with an ideal system. RMS re- projection pixel error in quadric transfer of camera pixels to projector pixels.

"... In PAGE 10: ... Projector internals and externals are then found from triangulated 3D points and corresponding projector im- age checker corner pixels. Table1 shows the results of theo- retical pixel re-projection errors for the linear estimation of Q before and after non-linear refinement. The setup contains four projectors, Proj1 and Proj3 were closer to the camera(- pair).... ..."

### Table 4. Maximum error and order of convergence for problems with discontin- uous diffusion coefficient with Dirichlet boundary conditions on refined grids.

"... In PAGE 20: ... We solve this problem with Dirichlet boundary conditions for partic- ular values of diffusion coefficient k1 = 1, k2 = 2. The convergence analysis for three examples with a discontinuous coefficient is presented in Table4 and confirms that our method is exact for even for non-smooth piecewise linear solutions and second order for non-linear solutions even in case of discontinuous diffusion... ..."

### Table 4 Effect of truncating the nonlinear flux on grid convergence: 112=2 case. Norm of

1998

"... In PAGE 8: ... The mesh-refinement was performed for several values of 112, and the finest grid contained 320 elements. Typical results, shown in Table4 for 112 6150, indicate that the convergence rate measured in the L49 norm drops to 25 112 when 77 61 784011259 10041 but is 25 112 4349 for all other cases. Figure 11 shows solutions for 112 6149and 112 61 50 (second and third order) in which the shock has formed and has begun to propagate.... ..."

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### Table 2: Conceptual Rules for Reservoirs in Parallel*

### Table 6 Goal refinement predicates Goal refinement

"... In PAGE 15: ... In partic- ular, our formal framework supports all phases of the require- ments analysis process described in the paper, including goal modeling. Thus, firstly, we introduce predicates for goal/task refinement and resource decomposition ( Table6 ). Predicate service(s) holds if s is a service.... ..."

Cited by 2