{"schema_version":"1.0","canonical_url":"https://patentable.app/patents/US-8516029","patent":{"patent_number":"US-8516029","title":"Methods and apparatuses for solving graph Laplacians","assignee":null,"inventors":[],"filing_date":"2009-06-12T00:00:00.000Z","publication_date":"2013-08-20T00:00:00.000Z","cpc_codes":["G06F"],"num_claims":35,"abstract":"Methods and apparatuses for solving a system on a symmetric diagonally dominant matrix. The method includes constructing an equivalent symmetric diagonally dominant linear system Ax=b from the system on a symmetric diagonally dominant matrix, wherein the matrix A of the equivalent linear system Ax=b has negative off-diagonal entries and zero row sums; constructing a graph of the matrix A of the equivalent linear system; constructing a decomposition of the graph; constructing a two-level process using the decomposition of the graph, wherein the two-level process includes reducing the equivalent linear system Ax=b to a linear system By=c; and extending the two-level process to a multi-level process having more than two levels."},"analysis":{"summary":null,"layman_explanation":null,"technical_analysis":null,"business_analysis":null,"faqs":null,"topics":[],"tech_cluster":null},"seo":{"title":"Methods and apparatuses for solving graph Laplacians","description":"Methods and apparatuses for solving a system on a symmetric diagonally dominant matrix. The method includes constructing an equivalent symmetric diagonally dominant linear system Ax=b from the system ","keywords":[]},"attribution":{"source":"Patentable","source_url":"https://patentable.app","canonical_url":"https://patentable.app/patents/US-8516029","license":"CC-BY-4.0-like","license_terms":"AI-generated analysis on this page (summary, layman_explanation, technical_analysis, business_analysis, faqs) may be reused with attribution and a visible link back to the canonical URL above. Patent abstracts, claims, and bibliographic data are USPTO public domain.","required_link":"https://patentable.app/patents/US-8516029","citation_suggestion":"Patentable. \"Methods and apparatuses for solving graph Laplacians\" (US-8516029). https://patentable.app/patents/US-8516029","copyright_holder":"Nomic Interactive Technology LLC"},"links":{"html":"https://patentable.app/patents/US-8516029","json":"https://patentable.app/api/llm-context/US-8516029","site":"https://patentable.app","llms_txt":"https://patentable.app/llms.txt"},"generated_at":"2026-05-31T21:55:35.700Z"}