<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<style type="text/css" style="display:none;"> P {margin-top:0;margin-bottom:0;} </style>
</head>
<body dir="ltr">
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
I have made a little more progress for the curious. First, taking only the real component is quite important. It stabilizes the complexity of the evalues significantly of course. I now take the real evalues and those that pass a very stringent CW test. For
comparing to the effective mass, I take the E_0 from all remaining evalues whose jackknife samples are within the plot windows. You can see them plotted between an estimate of mean/error from standard deviation and from a maybe still incorrect 60% confidence
window the authors suggest.</div>
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
With the larger momentum pz=2,3 where we may have wished we used momentum smearing, you can begin to see the advantage creep in. By tmax=21, the effective mass is lost, but the Lanczos result sometimes is quite stable. There are still occasional cases you can
see where the spread of the energies I get are quite wild. I haven't quite understood this yet.</div>
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<div class="elementToProof" style="font-family: Aptos, Aptos_EmbeddedFont, Aptos_MSFontService, Calibri, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
It would be nice to discuss more what problems can come in from the noise or another problem which may bias this. Take a look at<a href="https://arxiv.org/pdf/2407.21777" id="LPlnk250522" class="OWAAutoLink">https://arxiv.org/pdf/2407.21777</a> which as more
details then the original.</div>
<div id="appendonsend"></div>
<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Joseph Karpie<br>
<b>Sent:</b> Tuesday, August 20, 2024 5:05 PM<br>
<b>To:</b> Joseph Karpie via Hadstruct <hadstruct@jlab.org><br>
<b>Subject:</b> Lanczos for ground state energy</font>
<div> </div>
</div>
<style type="text/css" style="display:none">
<!--
p
{margin-top:0;
margin-bottom:0}
-->
</style>
<div dir="ltr">
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
Hey,</div>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
I have started testing the Lanczos idea for analyzing 2pt functions. I put basic formula and results into slides
<a href="https://docs.google.com/presentation/d/1uaQpQhQawA7VGA--2cjqrsSCSPoB6ORvl2M9iQZD4dQ/edit?usp=sharing" id="LPlnkOWAb922fa4f-4a76-b2a9-3bcc-f0ff1fdf9dbd" class="x_OWAAutoLink">
https://docs.google.com/presentation/d/1uaQpQhQawA7VGA--2cjqrsSCSPoB6ORvl2M9iQZD4dQ/edit?usp=sharing</a> I'm happy with the results given how roughly they are made. In the plot of evalues, and considering physical evalues must be positive and real, you can
tell most of them are garbage. I can explain the dirty filtering procedure I did tomorrow morning. I hope to actually do the more professional diagnostics in a next attempt. Unfortunately without going to longer times, this data doesn't actually reach the
regime where the advantage is significant.</div>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
Best,</div>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
Joe</div>
<div class="x_elementToProof" style="font-family:Aptos,Aptos_EmbeddedFont,Aptos_MSFontService,Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">
<br>
</div>
<div id="x_Signature" style="color:inherit">
<div style="font-family:Arial,Helvetica,sans-serif; font-size:9.75pt; color:rgb(34,34,34)">
<span style="background-color:rgb(255,255,255)">--</span></div>
<div style="direction:ltr; text-align:left; font-family:Arial,Helvetica,sans-serif; font-size:9.75pt; color:rgb(34,34,34)">
Joe Karpie</div>
<div style="direction:ltr; text-align:left; font-family:Arial,Helvetica,sans-serif; font-size:9.75pt; color:rgb(34,34,34)">
Pronouns: He/His/Him</div>
<div style="direction:ltr; text-align:left; font-family:Arial,Helvetica,sans-serif; font-size:9.75pt; color:rgb(34,34,34)">
Postdoctoral Fellow</div>
<div style="direction:ltr; text-align:left; font-family:Arial,Helvetica,sans-serif; font-size:9.75pt; color:rgb(34,34,34)">
Theoretical and Computational Physics Center</div>
<div style="direction:ltr; text-align:left; font-family:Arial,Helvetica,sans-serif; font-size:9.75pt; color:rgb(34,34,34)">
Jefferson Lab</div>
<span style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)"><br>
</span></div>
</div>
</body>
</html>