### Table XI. Performance of the pixel-based approach transformation from a cluster of ColorChecker DC broad-band digital signals (2 sets of filtered and unfiltered RGB) to reflectance applied to all targets using pseudo-inverse method.

### Table 13: Comparison of iterate method using CS-RBF and inverse MQ.

in Recent Developments in the Dual Receiprocity Method Using Compactly Supported Radial Basis Functions

### Table 13: Comparison of iterate method using CS-RBF and inverse MQ

in Recent Developments in the Dual Receiprocity Method Using Compactly Supported Radial Basis Functions

### Table 5.1 Null vectors from various Krylov subspace methods using the inverse-iteration and matrix-transpose ap- proaches.

2006

### Table 1: Coverages (%) of con dence interval methods for the adjustment coe cient. The numbers give are the empirical proportion of times that con dence limits 5 and 95 exceeded the true value of , for various bootstrap methods of interval construction. Details of the basic and test inversion methods are given in the text, the percentile and studentized methods are described in Chapter 5 of Davison and Hinkley (1997), and the NPI and NJK methods are described in Pitts et al. (1996). 5% 95%

"... In PAGE 10: ...f Pitts et al. (1996), on the original and on the log scales. We then used these intervals to estimate coverages for the various methods. Table1 about here With this particular setup we sometimes found bootstrap samples whose means y were positive, so the corresponding values of ^ were equal to zero; we did not use these resamples. Furthermore, the NJK intervals could not be calculated for 23 of the 1600 samples, due to the value of ^ depending too heavily on a single observation, and these samples do not contribute to the coverages for the NJK method.... In PAGE 10: ... Furthermore, the NJK intervals could not be calculated for 23 of the 1600 samples, due to the value of ^ depending too heavily on a single observation, and these samples do not contribute to the coverages for the NJK method. Table1 gives the percentages of the samples for which the true was less than its 5% and 95% con dence limits. A perfect method would have corresponding values 5 and 95, but none of the methods is perfect.... In PAGE 12: ...ines show probabilities 0.05 and 0.95, from which we read o the end-points of the intervals. Table1 : Coverages (%) of con dence interval methods for the adjustment coe cient. The num- bers give are the empirical proportion of times that con dence limits 5 and 95 exceeded the true value of , for various bootstrap methods of interval construction.... ..."

### Table 6: Equations for the inverse kinematic task. Average Abs. Error Relative Error Method

1995

Cited by 4

### Table 2: Expected complexity of several algorithms for computing mP with Algorithm 1 (A1) Method Multiplication Squaring Inversion PP

"... In PAGE 7: ...i.e. computing 2siQi) of the representation of m in each iteration. Thus, we can use our Algorithm 1 for speeding up the computation of mP. In Table2 we summarize the expected time complexity of several algorithms for computing mP with their respective number of precomputed points (PP). A detailed analysis of the k-ary method and the signed binary window method can be found in [3, 4, 5, 7].... In PAGE 7: ... We compare the 4-ary method combined with Algorithm 1 to M uller apos;s algorithms and the binary method. According to Table2 , if we assume r1 = 25, r2 = 1 and m about 200 bits, then we expect that the 4-ary method (with Algorithm 1) to be approximately 48% faster than the standard algorithm and 29% faster than M uller apos;s algorithm (the improved 2-ary). For applications such as smart cards, where storage space is limited, the 2-ary method (with Algorithm 1) is slightly faster than M uller apos;s algorithm (the improved 2-ary).... ..."

### Table 3. Results on Inverse Problem

1983

"... In PAGE 7: ... [8]) in the range [-10, 10] have been also added onto the instructions set. In Table3 , the performances on the inverse problem with different combinations of predictors are presented. As previously, for similar reasons, we see that the classical Top of stack and WTA methods works badly.... ..."

Cited by 1

### Table 1: Number of MVs and number of iterations (MVs/Iterations) to reduce the residual to 10?10 when searching for the largest (in absolute value) eigenvalue. The results are given for exact inversions and Method 1 and Method 2 with m iterations GMRES. The star denoted entries indicate that a di erent eigenvalue was found than the largest (misconvergence).

2000

"... In PAGE 13: ...ere added a bound on m. This gives us Method 2. Which we will compare to Method 1 for the same m. Table1 gives the total number of matrix vector multiplications (MVs) and JD iterations necessary to reduce the residual of eigenvector approximation to 10?10 for some matrices from the Matrix Market. We see from Table 1 that using the dynamic tolerance can in some cases improve the required number of MVs signi cantly.... In PAGE 13: ... Table 1 gives the total number of matrix vector multiplications (MVs) and JD iterations necessary to reduce the residual of eigenvector approximation to 10?10 for some matrices from the Matrix Market. We see from Table1 that using the dynamic tolerance can in some cases improve the required number of MVs signi cantly. For the PLAT1919 matrix and m = 5 even with a factor of more than 5.... ..."

### Table 1: Inverse Table

1998

"... In PAGE 4: ...e., truncn(sd; 8), page 11) in Table1 . The table maps each of the 128 8-bit non-0 signi cands to an 8-bit approximation of its reciprocal.... In PAGE 7: ... At line 6 the variable sd2 is assigned a 32,,17 oating point number that (we will prove) is 1=d with a relative error less than 2?28. This is done by obtaining an initial approximation via Table1 and then re ning it with two iterations of an easily computed variation of the Newton-Raphson method, sdi+1 = sdi(2 ? sdi d) (0 i 1): The variation is obtained by making the following transformations on the equation above. Instead of d we use the oating point number obtained by rounding d with the mode [away 32], i.... In PAGE 26: ...26 It is helpful to generalize away from the particulars of Table1 . Therefore, consider any table mapping keys to values.... In PAGE 26: ... Thus, if a table is quot;-ok and it contains a value v for truncn(d; 8) then jdv ? 1j lt; quot;. It is easy to con rm by computation that Table1 is quot;-ok for quot; = 3=512 and that it contains an entry assigning a value for the 8-bit truncation of every 1 d lt; 2 (e.g.... In PAGE 26: ...roved. Q.E.D. Perhaps the most interesting aspect of checking this proof mechanically is the quot;-ok prop- erty of Table1 . Just as described above, we de ned this property as an ACL2 (Common Lisp) predicate and proved the general lemma stating that any table satisfying that predicate gives su ciently accurate answers.... In PAGE 26: ... Just as described above, we de ned this property as an ACL2 (Common Lisp) predicate and proved the general lemma stating that any table satisfying that predicate gives su ciently accurate answers. When the general lemma is applied to our particular lookup, the system executes the predicate on Table1 to con rm that it has the required property.... In PAGE 27: ...27 var = value error bounds sd0 = (1=d)(1 + quot;sd0(d)) j quot;sd0(d)j lt; 2?8 + 2?9 sdd0 = 1 + quot;sdd0(d) quot;sd0(d) quot;sdd0(d) quot;sd0(d) + 2?30 sd1 = (1=d)(1 ? quot;sd1(d)) 0 quot;sd1(d) quot;sd0(d)2 + sdd1 = (1 ? quot;sdd1(d)) quot;sd1(d) ? 2?30 quot;sdd1(d) quot;sd1(d) sd2 = (1=d)(1 ? quot;sd2(d)) 0 quot;sd2(d) quot;sd1(d)2 + Table 2: Error Analysis for Lines 1-6 ( = 2?29 + 2?31 + (9=512)2?31) the particulars of Table1 are involved in the proof is when the predicate is executed. This example illustrates the value of computation in a general-purpose logic.... ..."

Cited by 27