Construction of H-Symmetric pentadiagonal matrices by three spectra

Figures & data

Table 1. Numerical results for Example 3.1 without modified Gram–Schmidt method.

n	$\Vert \sigma (P^{(c)})-\sigma (P)\Vert$	$\Vert {\sigma }_1(P^{(c)})-{\sigma }_1(P)\Vert$	$\Vert {\sigma }_2(P^{(c)})-{\sigma }_2(P)\Vert$
10	1.41e$-07$	1.37e$-07$	1.45e$-07$
50	165.59	166.77	166.88
100	337.07	338.06	338.20
200	374.86	375.59	375.72

Table 2. Numerical results for Example 3.1 with applying modified Gram–Schmidt method.

n	$\Vert \sigma (P^{(c)})-\sigma (P)\Vert$	$\Vert {\sigma }_1(P^{(c)})-{\sigma }_1(P)\Vert$	$\Vert {\sigma }_2(P^{(c)})-{\sigma }_2(P)\Vert$
10	4.06e−14	1.19e−14	9.74e−15
50	1.35e−13	3.12e−14	3.50e−14
100	1.55e−13	4.12e−14	4.35e−14
200	4.30e−13	5.51e−14	5.71e−14

Table 3. Numerical results for Example 3.2 without Modified Gram–Schmidt method.

n	$\Vert \sigma (P^{(c)})-\sigma (P)\Vert$	$\Vert {\sigma }_1(P^{(c)})-{\sigma }_1(P)\Vert$	$\Vert {\sigma }_2(P^{(c)})-{\sigma }_2(P)\Vert$
10	2.16e−12	2.22e−12	2.33e−12
50	7.0467	5.5257	5.5861
100	52.7912	52.6453	52.7120
200	77.5283	77.4396	77.4848

Table 4. Numerical results for Example 3.2 with applying Modified Gram–Schmidt method.

n	$\Vert \sigma (P^{(c)})-\sigma (P)\Vert$	$\Vert {\sigma }_1(P^{(c)})-{\sigma }_1(P)\Vert$	$\Vert {\sigma }_2(P^{(c)})-{\sigma }_2(P)\Vert$
10	5.48e−14	4.48e−14	3.80e−14
50	2.38e−13	2.00e−13	1.82e−13
100	2.75e−13	3.62e−13	2.68e−13
200	1.05e−12	5.86e−13	5.19e−13

Table 5. Numerical results for Example 3.3 without Modified Gram–Schmidt method.

n	$\Vert \sigma (P^{(c)})-\sigma (P)\Vert$	$\Vert {\sigma }_1(P^{(c)})-{\sigma }_1(P)\Vert$	$\Vert {\sigma }_2(P^{(c)})-{\sigma }_2(P)\Vert$
10	2.86e−12	2.68e−12	2.17e−12
50	2.57e−04	2.96e−04	2.71e−04
100	37.84	32.82	32.99
200	106.71	104.99	105.15

Table 6. Numerical results for Example 3.3 with applying Modified Gram–Schmidt method.

n	$\Vert \sigma (P^{(c)})-\sigma (P)\Vert$	$\Vert {\sigma }_1(P^{(c)})-{\sigma }_1(P)\Vert$	$\Vert {\sigma }_2(P^{(c)})-{\sigma }_2(P)\Vert$
10	7.87e−14	9.90e−14	1.29e−14
50	3.86e−13	4.99e−13	3.84e−13
100	9.60e−13	6.07e−13	5.95e−13
200	2.05e−12	1.07e−12	1.02e−12