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<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times">Hello all,</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times"><br>
</font></div>
<div><font face="Times">I am diagonalizing a <i style="color: rgb(0, 0, 0); font-size: 14px;">
hermitian</i> matrix (<span style="background-color: rgb(255, 255, 255);"><b>MatIsHermitian = 1
</b>up to a tolerance of <b>1e-15</b></span>) using <i style="color: rgb(0, 0, 0); font-size: 14px;">
krylovschur</i>, with <i style="color: rgb(0, 0, 0); font-size: 14px;">EPS_TARGET_MAGNITUDE = 0, </i>but getting
<b>complex eigenvalues</b>. Also, I am getting seemingly spurious eigenvalues of magnitude very close to 0, whose relative errors are much larger than my set tolerance. Can anyone indicate what might be the cause and possible solutions.</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times"><br>
</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times">I have attached the files <i>eps_view</i>,
<i>A_mat_binary</i>, and <i>B_mat_binary </i>files, which show the settings I have used, and contain the A and B matrices respectively (in binary).</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times"><br>
</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times">The eigenvalues I get are:</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times"><br>
</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;">
<div><font face="Times"> # <span class="Apple-tab-span" style="white-space:pre">
</span> <span class="Apple-tab-span" style="white-space:pre"></span> <span class="Apple-tab-span" style="white-space:pre">
</span> Eigenvalue</font></div>
<div><font face="Times"> —<span class="Apple-tab-span" style="white-space:pre"> </span>
----------------------------------------------------------------</font></div>
<div><font face="Times"> 0 0.0000000000000077 + i -0.0000000000000000</font></div>
<div><font face="Times"> 1 0.0000000000000265 + i -0.0000000000000008</font></div>
<div><font face="Times"> 2 0.0000000000000340 + i 0.0000000000000002</font></div>
<div><font face="Times"> 3 0.0000000000000373 + i 0.0000000000000001</font></div>
<div><font face="Times"> 4 0.0000000000000444 + i -0.0000000000000007</font></div>
<div><font face="Times"> 5 0.0000000000000448 + i -0.0000000000000017</font></div>
<div><font face="Times"> 6 0.0000000000000470 + i 0.0000000000000002</font></div>
<div><font face="Times"> 7 0.0000000000000489 + i 0.0000000000000030</font></div>
<div><font face="Times"> 8 0.0000000000000548 + i 0.0000000000000006</font></div>
<div><font face="Times"> 9 0.0000000000000585 + i 0.0000000000000001</font></div>
<div><font face="Times"> 10 0.0000000000000643 + i 0.0000000000000005</font></div>
<div><font face="Times"> 11 0.0000000000000714 + i -0.0000000000000008</font></div>
<div><font face="Times"> 12 0.0000000000000750 + i -0.0000000000000019</font></div>
<div><font face="Times"> 13 0.0000000000000752 + i 0.0000000000000031</font></div>
<div><font face="Times"> 14 0.0000000000000769 + i -0.0000000000000002</font></div>
<div><font face="Times"> 15 0.0000000000000784 + i -0.0000000000000037</font></div>
<div><font face="Times"> 16 0.0000000000000860 + i 0.0000000000000002</font></div>
<div><font face="Times"> 17 0.0000000000000880 + i -0.0000000000000004</font></div>
<div><font face="Times"> 18 0.0000000000000968 + i -0.0000000000000001</font></div>
<div><font face="Times"> 19 0.0000000000000979 + i 0.0000000000000013</font></div>
<div><font face="Times"> 20 0.0000000000001045 + i -0.0000000000000001</font></div>
<div><font face="Times"> 21 0.0000000000001150 + i -0.0000000000000011</font></div>
<div><font face="Times"> 22 0.0000000000001348 + i -0.0000000000000012</font></div>
<div><font face="Times"> 23 0.0000000000001446 + i -0.0000000000000019</font></div>
<div><font face="Times"> 24 0.0000000000001454 + i 0.0000000000000011</font></div>
<div><font face="Times"> 25 0.0000000000001555 + i 0.0000000000000003</font></div>
<div><font face="Times"> 26 0.0000000000002513 + i -0.0000000000000009</font></div>
<div><b><font face="Times"> 27 5.0908854514230413 + i -0.0022004178122762</font></b></div>
<div><b><font face="Times"> 28 5.2768106039842175 + i 0.1043464906789375</font></b></div>
<div><b><font face="Times"> 29 5.3003883062604187 + i -0.0757735907905433</font></b></div>
<div><b><font face="Times"> 30 11.5143655883932929 + i 0.0049838692042474</font></b></div>
<div><b><font face="Times"> 31 11.8821523259838653 + i -0.1475608751440501</font></b></div>
<div><b><font face="Times"> 32 11.9515216995487101 + i 0.1857395729336506</font></b></div>
<div><b><font face="Times"> 33 12.0909362158339384 + i 0.0049114285397287</font></b></div>
<div><b><font face="Times"> 34 12.0905704159492675 + i -0.1522880348537981</font></b></div>
<div><b><font face="Times"> 35 12.2205398661469111 + i -0.0781999802933937</font></b></div>
<div><b><font face="Times"> 36 12.4807156964720480 + i -0.2850122604907908</font></b></div>
<div><b><font face="Times"> 37 12.6082849940660289 + i 0.0560456679728079</font></b></div>
<div><b><font face="Times"> 38 12.9384278480576125 + i 0.0238826907631012</font></b></div>
<div><b><font face="Times"> 39 17.5230234731441357 + i -0.1824807274488794</font></b></div>
<div><b><font face="Times"> 40 17.5503678395543901 + i 0.1785356473404145</font></b></div>
<div><b><font face="Times"> 41 17.6933953160112409 + i -0.0626631055149425</font></b></div>
<div><b><font face="Times"> 42 19.1692824404480930 + i -0.6351729266691462</font></b></div>
<div><b><font face="Times"> 43 19.4158452684509797 + i 0.3151965488807310</font></b></div>
<div><b><font face="Times"> 44 19.6020750507704591 + i -0.2559887580276014</font></b></div>
<div><b><font face="Times"> 45 19.6443102906562181 + i 1.1005601705485646</font></b></div>
<div><b><font face="Times"> 46 19.7948713379697452 + i 0.1230015140422697</font></b></div>
<div><b><font face="Times"> 47 19.8791098474284347 + i -0.1943322911563744</font></b></div>
<div><b><font face="Times"> 48 20.1268732265661860 + i -0.0340890856219265</font></b></div>
<div><b><font face="Times"> 49 20.1368588182453898 + i 0.2673370459460956</font></b></div>
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<div style="color: rgb(0, 0, 0); font-size: 14px;"><b><font face="Times"><br>
</font></b></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><b><font face="Times"><br>
</font></b></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times">Thanks in advance,</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times">Sidd</font></div>
<div style="color: rgb(0, 0, 0); font-size: 14px;"><font face="Times">Worcester Polytechnic, U.S.A.</font></div>
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