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Table 4 Characteristics of preconditioned (deflated) coefficient matrices, and of PCG and DPCG methods for the field dataset

From: Deflated preconditioned conjugate gradient method for solving single-step BLUP models efficiently

Model

Methoda

Smallest eigenvalue

Largest eigenvalue

Effective condition number

Number of iterationsb

Total timec

Time/iterationd

ssGBLUP

PCG

2.3 × 10−5

5.1

2.2 × 105

729

3993

5.3 (0.4)

ssSNPBLUP

PCG

3.7 × 10−5

1751.9

4.7 × 107

10,000

52,683

4.4 (0.4)

 

DPCG (200)

1.2 × 10−5

193.1

1.6 × 107

10,000

92,171

9.2 (1.4)

 

DPCG (50)

8.7 × 10−6

29.9

3.4 × 106

6074

52,503

8.6 (2.4)

 

DPCG (5)

2.9 × 10−5

4.8

1.7 × 105

748

7735

8.7 (0.3)

ssPCBLUPe

PCG

1.2 × 10−5

220.0

1.8 × 107

10,000

30,198

2.9 (0.2)

 

DPCG (200)

8.3 × 10−6

113.3

1.4 × 107

10,000

58,280

5.8 (0.7)

 

DPCG (50)

7.7 × 10−6

46.0

6.0 × 106

8541

55,388

6.5 (0.5)

 

DPCG (5)

8.0 × 10−6

5.1

6.4 × 105

2686

15,063

5.6 (0.2)

 

DPCG (1)

9.6 × 10−4

4.8

4.9 × 104

375

2402

6.3 (0.2)

  1. aNumber of SNP effects per subdomain is within brackets
  2. bA number of iterations equal to 10,000 means that the method failed to converge within 10,000 iterations
  3. cWall clock time (s) for the iterative process
  4. dAverage wall clock time (s) (SD within brackets) per iteration. Iterations computing the residual from the coefficient matrix for the PCG method were removed before averaging
  5. eThe number of principal components retained was equal to 13,803