### Table 2 Asymptotic Covariance Matrix of Singular Values

1997

Cited by 1

### Table 2 Asymptotic Covariance Matrix of Singular Values

1997

Cited by 1

### Table 6 Intervals for Polynomial Acceleration within TRSVD.

1992

"... In PAGE 17: ...n (18) becomes much easier to solve, i.e., 0 @ I Pq( ~ B)Yk Y T k Pq( ~ B) 0 1 A 0 @ d(k) jl 1 A = 0 @ y(k) j0 1 A ; j = 1; 2; : : :; p: (25) It is easy to show that the updated eigenvector approximation, y(k+1) j , is determined by y(k+1) j = y(k) j ? d(k) j = Pq( ~ B)Yk hY T k P2 q ( ~ B)Yki?1 Y T k Pq( ~ B)y(k) j : Thus, we need not employ the use of an iterative solver for determining Yk+1 since the matrix hY T k P2 q ( ~ B)Yki?1 is of order p and using the orthogonal factorization Pq( ~ B)Yk = ^ Q ^ R ; we have hY T k P2 q ( ~ B)Yki?1 = ^ R?T ^ R?1 : The control of the polynomial degree, q, is determined by the strategy discussed in [37] and [4]. Table6 lists three possible intervals for damping the unwanted singular values of A which correspond to the choice of H in (11). If we choose H = ~ B, then for the TRSVD iteration in polynomial aceleration starts, we apply Pq(B), where B is the 2-cyclic matrix in (5).... ..."

Cited by 4

### Table 3 Singular values sp71 of initial matrix A

2000

"... In PAGE 13: ... In the same way, every increase of n}inps was subject to the restriction that it must be separated from the previous one by at least 20 iterations, except in the n}inps quot;1ton}inps quot;2 case. The most relevant singular values for the quot;rst execution of SVD plus QR-cp within the algorithm are given in Table3 . Note that matrix A is clearly ill-conditioned, since according to the table, cond(A) quot;sp16/sp16p24 must be at least 550 (in fact, the real value for the condition of A is nearly 2.... ..."

### Table 2: Test matrices for the singular value decomposition

1997

"... In PAGE 25: ...14 Tests for the ScaLAPACK SVD routines The following tests will be performed on PDGESVD. A number of matrix #5Ctypes quot; are speci#0Ced, as denoted in Table2 . For each type of matrix, and for the minimal workspace as well as for larger than minimal workspace an M-byN matrix #5CA quot; with known singular... In PAGE 26: ....14.1 Test Matrices for the Singular Value Decomposition Routines Six di#0Berenttypes of test matrices may be generated for the singular value decomposition routines. Table2 shows the types available, along with the numbers used to refer to the matrix types. Except as noted, all matrix types other than the random bidiagonal matrices have O#281#29 entries.... ..."

### Table 1. Singular Value Decomposition of global design matrix as given by their singular eigenvalues.

165

### Table 7 Errors of singular values for Example 3

1992

"... In PAGE 18: ... Nevertheless, once convergence occurs, then from (91) weknow that must be a subset of the singular values of the nal matrix. Table7 displays the 2-norm of the vector ( ) ; throughout the iteration. It is seen that at the initial stage the convergence is slow, but eventually the rate picks up and becomes quadratic.... ..."

Cited by 11

### Table 7 Errors of singular values for Example 3

"... In PAGE 18: ... Nevertheless, once convergence occurs, then from (91) we know that must be a subset of the singular values of the nal matrix. Table7 displays the 2-norm of the vector ( ) ? throughout the iteration. It is seen that at the initial stage the convergence is slow, but eventually the rate picks up and becomes quadratic.... ..."

### Table 2: Impact of noise on singular values

"... In PAGE 5: ... Figure 2: Three views of the logo of our institute Now, we demonstrate the performance when a zero mean random noise is added to the position of the synthetically transformed shape for an affine homography. The two sin- gular values of interest of matrix a152 for different noise levels for real(without quantization) and discrete (integers) bound- ary representations are shown in Table2 . This ratio does deteriorate with noise, however, there was still more than an order of magnitude separation between them even with a noise of 20% in the positions of the boundary points.... ..."

### Table 2: Impact of noise on singular values

"... In PAGE 5: ... Figure 2: Three views of the logo of our institute Now, we demonstrate the performance when a zero mean random noise is added to the position of the synthetically transformed shape for an affine homography. The two sin- gular values of interest of matrix a155 for different noise levels for real(without quantization) and discrete (integers) bound- ary representations are shown in Table2 . This ratio does deteriorate with noise, however, there was still more than an order of magnitude separation between them even with a noise of 20% in the positions of the boundary points.... ..."