Table 1 Residual and CPU time in seconds for solving Example 3.1 by four methods for different sizes.

From: Two fast algorithms for finding the solution of the lower Hessenberg quasi-Toeplitz linear system from Markov chain

n

Back-slash

QR

LU

Our Algorithm 1

Our Algorithm 2

RES

Time (s)

RES

Time (s)

RES

Time (s)

RES

Time (s)

RES

Time (s)

\(2^{10}\)

2.3315e−15

0.0170

2.3315e−15

0.0155

5.8842e−15

0.0732

3.0254e−15

0.0065

2.6923e−15

0.0084

\(2^{11}\)

3.4417e−15

0.1245

3.4417e−15

0.0965

7.1054e−15

0.4303

6.8834e−15

0.0094

6.9944e−15

0.0123

\(2^{12}\)

5.7732e−15

0.7712

5.7732e−15

0.5901

1.2546e−14

3.0541

4.5519e−15

0.0192

4.4409e−15

0.0253

\(2^{13}\)

9.5479e−15

5.0455

1.0325e−14

4.4950

2.4536e−14

23.0388

9.4411e−14

0.0419

9.4050e−14

0.0466

\(2^{14}\)

1.2990e−14

34.5136

1.2990e−14

34.6899

3.4195e−14

172.4416

7.3497e−14

0.0637

7.3275e−14

0.0698