### Table 2: The values of used for the 2 2 sensor array with the periodic boundary condition.

in Wavelet Deblurring Algorithms for Spatially Varying Blur from High-Resolution Image Reconstruction

2003

"... In PAGE 11: ... Figure 3 depicts the reconstructed high-resolution image with noise at PSNR = 30dB. The values of the parameter used in our algorithm are given in Table2 for reference. Least Squares Model Our Algorithm SNR(dB) PSNR RE PSNR RE Iterations 30 28.... ..."

### Table 2: The values of used for the 2 2 sensor array with the periodic boundary condition.

in Wavelet Deblurring Algorithms for Spatially Varying Blur from High-Resolution Image Reconstruction

"... In PAGE 11: ... Figure 3 depicts the reconstructed high-resolution image with noise at PSNR = 30dB. The values of the parameter used in our algorithm are given in Table2 for reference. Least Squares Model Our Algorithm SNR(dB) PSNR RE PSNR RE Iterations 30 28.... ..."

### Table 2. Boundary Conditions, Stress Periods During Pumping Test

"... In PAGE 2: ... Because no natural hydrologic boundaries are located in the vicinity of the test location, the model boundaries are conceptualized as constant groundwater heads that change with time between stress periods. The model was fully transient with multiple stress periods (pumping intervals), and consisted of constant head boundaries that changed in head value between stress periods ( Table2... ..."

### Table 2: Di erent Petsc KSP Objects Results complex computation problems has been done with non periodic boundary condition with introduc- ing a decomposition of the operator into a set of homogeneous problems with Dirichlet boundary conditions, solve once for all, and a time dependant inhomogeneous problem with periodic boundary conditions. We attempt to use the PETSc 2.0 library in order to implicit further our scheme. The implementation of the method with this library provides goods accuracy agreement, but not yet good parallelism e ciency.

"... In PAGE 4: ... Once the numerical algorithm will be choosen, we will further enhance the performances of the implementation. Table2 described the results reached with various KSP objects of the Petsc library on the test case matrix. We xed the (r)elative, (a)bsolute, and (d)ivergence tolerances for the convergence.... ..."

### Table 4: Cache oblivious performance for four itera- tions of varying problem sizes on the Itanium 2, with non-periodic boundary conditions. Despite large re- ductions in cache misses, the cache oblivious algo- rithm performs up to 45% slower.

2006

Cited by 4

### TABLE 1: Numbers C(M,N) of Configuration Classes for the One-Dimensional Lattice System, with Nearest-Neighbor Exclusions, and Periodic Boundary Conditions M N ) 2 N ) 3 N ) 4 N ) 5 N ) 6 N ) 7 N ) 8

2004

Cited by 1

### Table 2: L1 Errors of solving wave equation with non-periodic boundary conditions using schemes with numerical boundary closures. The initial condition is u(x; 0) = sin(! x). The results correspond to test cases of di erent values of ! with a xed number of grids N in a xed computational domain (0; 1). L= x is the number of grids used to resolve one wave period in space, where L = 2 =!, a = 0, b = 1, and N = 50.

"... In PAGE 18: ... The fourth-order boundary schemes are used because the inner scheme is fourth-order accurate and fth-order boundary schemes are unstable. Table2 shows the errors of the numerical solutions using the three schemes with boundary closures. The results show that, the seventh-order upwind compact and explicit schemes are much more accurate for small ! as expected.... ..."

### Table 3: Damping factors of the error in the Jacobi iteration. The same wavelets, D6, are used for both the central di erence and the Galerkin discretizations. As long as periodic boundary conditions are used, the wavelet based preconditioners achieve bounded condition numbers. The implementation of other boundary condi- tions does not produce the same kind of results. Experiments show that diagonal preconditioning of operators associated to Dirichlet boundary values compress the condition numbers from O( x?2) to O( x?1). This is an essential di erence from the Multigrid approach. In the Multigrid setting, the error equation is solved on each level Vj. If the original problem has Dirichlet boundary conditions, then Multigrid essentially solves problems with periodic (zero) boundary conditions. 60

1995

"... In PAGE 69: ...f 4. The same wavelets and operator LJ+1 as in Figure 17. In the experiments, we chose = 0:1 x2 and compared the preconditioned iterations for the central di erence approximation and the Galerkin discretization described in the previous section. The maximal eigenvalues of the iteration matrices (excepting the one corresponding to constant functions) are given in Table3 . These values are the bounds in the reduction of the error of the Jacobi iteration.... ..."

Cited by 8