Eigenvalues of symmetric matrices

Gordon Royle on Fri, 01 Dec 2023 03:43:21 +0100

[Date Prev] [Date Next] [Thread Prev] [Thread Next] [Date Index] [Thread Index]

Eigenvalues of symmetric matrices

To: "pari-users@pari.math.u-bordeaux.fr" <pari-users@pari.math.u-bordeaux.fr>
Subject: Eigenvalues of symmetric matrices
From: Gordon Royle <gordon.royle@uwa.edu.au>
Date: Fri, 1 Dec 2023 02:43:11 +0000
Accept-language: en-AU, en-US
Arc-authentication-results: i=1; mx.microsoft.com 1; spf=pass smtp.mailfrom=uwa.edu.au; dmarc=pass action=none header.from=uwa.edu.au; dkim=pass header.d=uwa.edu.au; arc=none
Arc-message-signature: i=1; a=rsa-sha256; c=relaxed/relaxed; d=microsoft.com; s=arcselector9901; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-AntiSpam-MessageData-ChunkCount:X-MS-Exchange-AntiSpam-MessageData-0:X-MS-Exchange-AntiSpam-MessageData-1; bh=csTzNDE7c705SZrXGXTk+wv2eCvMmkNLH3phHOD7pzE=; b=FwhzUETuPbnMR0xSojQsrGSQPjYH9gDmxYVFrvXUD7GKxW1CYXvlIoDnkZrJ1bpGY/BwT1HgF27uICMVjylHSducxEb3tTK0bx7VXj9QJH7Ve32mzIUhWyoygVAJycRG10LD30vQzNnwSU5tbP/lQgq2FxDSthL6hcT4GnMFg95C2OBLCx9e8DG42Aw8XWSHGbzeTIXFXanxQyfbZb4Z96PHcuKXRW979hT/iXB+DNOHjYYZUcTTBYMvdUvPjiGoXpWSOdaEdvaRibJTMXCUkD/5bbREaLVC82U+BeWkq7vjD8fmE+b1Fw+hzr60xpOgrEc/02cQibQLyPaq2bomzg==
Arc-seal: i=1; a=rsa-sha256; s=arcselector9901; d=microsoft.com; cv=none; b=TLLupjvLD6fH/i6SpnHzhyllZnOmpdNffkQIROScId85yRuH0x3/Q6K0b1lCGBAr1utd/JbOPQx0pT3x0jekBkfrJh8ZcelvokKpmTKCMxVJ4J0Oxlkg7pkTauke8lJbrIHgjeSCs50p/fSKcqA5SPvED1EzhddZtJ1duh6UgKWhFuL1+XXRVUUPsE67Fkj3JJG+dzHHykwYX150m4Gs9Tqi6uSvuWmoGkBnN4KpZTSDLRnu8AFW/2LVqoSvoQYKWxP5qs3akHHToe3fDX5CdZRqlVeWbAS+ELMINrx7vbefEf6jVY4ExbYZObSzQzWyB4FhW4aqiugfQSFEH4FgcA==
Authentication-results: dkim=none (message not signed) header.d=none;dmarc=none action=none header.from=uwa.edu.au;
Delivery-date: Fri, 01 Dec 2023 03:43:21 +0100
Dkim-signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=uwa.edu.au; s=selector2; h=From:Date:Subject:Message-ID:Content-Type:MIME-Version:X-MS-Exchange-SenderADCheck; bh=csTzNDE7c705SZrXGXTk+wv2eCvMmkNLH3phHOD7pzE=; b=szGikPuW5WXw8XltRAwF9sEtiWYTBirdciSU0x6goPnF+SLmkrGfeb06/8jt5JAuNVBEEkrj7tqgR9JMg4cCV6wpG8S1HbDIrUJnaRexEaCseIsMFLaV3YpV+IXHudkpAp5me51AEFEkiBg+XgFqbKyqZ22oEk+bx5/OCoIKXF8vkhnX+3xGX3jquvitzJwouduu3UYxjIeD6x+krgo0tXEgiDg4wqlf8E3xf1fEIiXgKwUWNLO00Y7VwimTb6yGXUot/AB06tefGmfwJuM/pV6QrDEChJm+Q+ptWdlNNy7blOmmUerFwd+164b76sP6a6dZzWJYNE+Rik6v9R3ZjA==
Thread-index: AQHaI/79vYHIAKWI/0KCVuym3DurHg==
Thread-topic: Eigenvalues of symmetric matrices

I am using Pari/GP to compute the eigenvalues of a large number (10s of millions) of symmetric 0/1-matrices of order about 24 x 24 to 30 x 30; the matrices are adjacency matrices of 3-regular graphs and so have exactly three 1s per row and column.

At the moment, I am just using polrootsreal(charpoly(a)), but I wonder if there is a faster way to do it?

Thanks

Gordon

Follow-Ups:
- Re: Eigenvalues of symmetric matrices
  - From: Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>

Next by Date: Re: foursquares.gp
Next by thread: Re: Eigenvalues of symmetric matrices
Index(es):
- Date
- Thread