### Table 4: AVP Scheme combined cost savings over BVP Scheme

1999

Cited by 14

### Table 2. Numerical results for \exterior quot; Dirichlet BVP.

1998

Cited by 14

### Table 3. Numerical results for \interior quot; Dirichlet BVP.

1998

"... In PAGE 28: ... Figure 6 c) shows the error in the case that the interface is given by 101 points. Table3 shows how the error behaves when the representation of the interface is improved; we see at least fourth order behavior which should not come as a surprise given the quality of interpolation by cubic splines. In the table, n1 is the number of points on the interface.... ..."

Cited by 14

### Table 3. The 3D results for mixed b.v.p.

1998

"... In PAGE 9: ...Table3 . The PMINRES iteration count seems to be constant even though Cl appears to be growing slightly when N is increased.... ..."

Cited by 8

### Table 4.3: Main algorithm for solving a BVP

### Table 3. The 3D results for mixed b.v.p.

"... In PAGE 9: ...Table3 . The PMINRES iteration count seems to be constant even though Cl appears to be growing slightly when N is increased.... ..."

### Table 3.1: Numerical results for \interior quot; Dirichlet BVP. n

### Table 3.3: Numerical results for \exterior quot; Dirichlet BVP. n

### Table 1: Errors and convergence rates with and without C1-spline smoothing for BVP (6).

"... In PAGE 5: ... Consider the two point boundary-value problem ?u00(x) + 2u(x) = 2 2 sin x; x 2 (0; 1); u(0) = u(1) = 0; (6) with solution u(x) = sin x. As computational grids Xk we take 2k+3 + 1 uniformly spaced points on [0; 1] as indicated in Table1 . Even though we are dealing with a one-dimensional problem we use the radial basis function 5;3 as de ned in Eqn.... In PAGE 6: ... We do this in order to keep the bandwidth of the system matrices constant (note that the mesh size is also halved in each iteration). The rightmost column of Table1 shows the percentage of nonzero entries in the system matrix at each level. Columns 2 and 3 of Table 1 show how the multilevel collocation al- gorithm performs without the recommended smoothing.... In PAGE 6: ... The rightmost column of Table 1 shows the percentage of nonzero entries in the system matrix at each level. Columns 2 and 3 of Table1 show how the multilevel collocation al- gorithm performs without the recommended smoothing. Clearly, it ceases to converge after the rst 4 steps.... In PAGE 6: ... In Fasshauer amp; Jerome[5] the smoothing speeds tk were de ned as tk = k, where the three parameters , and can be chosen by the user (with some dependency on the smoothness of the problem). For the results of Table1 we have used = 10, = 1:1, and = 1:2. The reader can see at least some bene ts of the smoothing in this example since the errors (as well as the convergence rates) are better for the rst few steps of smoothing.... In PAGE 7: ... Again, we use the RBF 5;3. The arrangement of the information in Table 2 is the same as in Table1 . However, the smoothing operation is now performed by convolving with the Gauss-Weierstrass kernel t(x) = t2 (4 )e?t2kxk2 4 ; x 2 IR2 : The parameters determining the smoothing speeds are = 1:2, = 1:5, and = 1:9.... ..."