{"version":"1.0","provider_name":"In Abstract","provider_url":"https:\/\/www.mub.eps.manchester.ac.uk\/in-abstract","author_name":"Enna Bartlett","author_url":"https:\/\/www.mub.eps.manchester.ac.uk\/in-abstract\/author\/ennabartlett\/","title":"A New Analysis of Iterative Refinement and its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems - In Abstract","type":"rich","width":600,"height":338,"html":"<blockquote class=\"wp-embedded-content\" data-secret=\"K354j1tzkl\"><a href=\"https:\/\/www.mub.eps.manchester.ac.uk\/in-abstract\/how-to-solve-sensitive-equations-accurately\/\">A New Analysis of Iterative Refinement and its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems<\/a><\/blockquote><iframe sandbox=\"allow-scripts\" security=\"restricted\" src=\"https:\/\/www.mub.eps.manchester.ac.uk\/in-abstract\/how-to-solve-sensitive-equations-accurately\/embed\/#?secret=K354j1tzkl\" width=\"600\" height=\"338\" title=\"&#8220;A New Analysis of Iterative Refinement and its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems&#8221; &#8212; In Abstract\" data-secret=\"K354j1tzkl\" frameborder=\"0\" marginwidth=\"0\" marginheight=\"0\" scrolling=\"no\" class=\"wp-embedded-content\"><\/iframe><script type=\"text\/javascript\">\n\/* <![CDATA[ *\/\n\/*! This file is auto-generated *\/\n!function(d,l){\"use strict\";l.querySelector&&d.addEventListener&&\"undefined\"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!\/[^a-zA-Z0-9]\/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret=\"'+t.secret+'\"]'),o=l.querySelectorAll('blockquote[data-secret=\"'+t.secret+'\"]'),c=new RegExp(\"^https?:$\",\"i\"),i=0;i<o.length;i++)o[i].style.display=\"none\";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute(\"style\"),\"height\"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):\"link\"===t.message&&(r=new URL(s.getAttribute(\"src\")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener(\"message\",d.wp.receiveEmbedMessage,!1),l.addEventListener(\"DOMContentLoaded\",function(){for(var e,t,s=l.querySelectorAll(\"iframe.wp-embedded-content\"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute(\"data-secret\"))||(t=Math.random().toString(36).substring(2,12),e.src+=\"#?secret=\"+t,e.setAttribute(\"data-secret\",t)),e.contentWindow.postMessage({message:\"ready\",secret:t},\"*\")},!1)))}(window,document);\n\/* ]]> *\/\n<\/script>\n","thumbnail_url":"https:\/\/www.mub.eps.manchester.ac.uk\/in-abstract\/wp-content\/uploads\/sites\/61\/2017\/11\/A-New-Analysis-of-Iterative-Refinement-and-its-Application-to-Accurate-Solution-of-Ill-Conditioned-Sparse-Linear-Systems.jpg","thumbnail_width":890,"thumbnail_height":350,"description":"How to Solve Sensitive Equations Accurately Some systems of linear equations are ill conditioned: a tiny change in the coefficients can produce a large change in the solution. There is growing interest in using lower precisions such as single or even half precision in climate and weather modeling and machine learning, but this brings an [&hellip;]"}