On Deflations in Extended QR Algorithms

نویسندگان

  • Thomas Mach
  • Raf Vandebril
چکیده

In this paper we discuss the deflation criterion used in the extended QR algorithm based on the chasing of rotations. We provide absolute and relative perturbation bounds for this deflation criterion. Further, we present a generalization of aggressive early deflation to the extended QR algorithms. Aggressive early deflation is the key technique for the identification and deflation of already converged, but hidden, eigenvalues. Often these possibilities for deflation are not detected by the standard technique. We present numerical results underpinning the power of aggressive early deflation also in the context of extended QR algorithms. We further generalize these ideas by the transcription of middle deflations.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Multilevel communication optimal LU and QR factorizations for hierarchical platforms

This study focuses on the performance of two classical dense linear algebra algorithms, the LU and the QR factorizations, on multilevel hierarchical platforms. We first introduce a new model called Hierarchical Cluster Platform (HCP), encapsulating the characteristics of such platforms. The focus is set on reducing the communication requirements of studied algorithms at each level of the hierar...

متن کامل

On the implementation of adaptive equalizers for wireless ATM with an extended QR-decomposition-based RLS-algorithm

An extended QR-decomposition (QRD)-based RLS-algorithm is introduced, applicable for equalization, allowing an estimate of the transmitted symbol, when it is a-priori unknown. To achieve low-cost implementations strength reduction and square-root free Givens-rotations are applied. Several QRD-based RLS-algorithms are compared in terms of the number of mathematical operations. The QR-RLS-algorit...

متن کامل

Performance Predictions of Multilevel Communication Optimal LU and QR Factorizations on Hierarchical Platforms

In this paper we study the performance of two classical dense linear algebra algorithms, the LU and the QR factorizations, on multilevel hierarchical platforms. We note that we focus on multilevel QR factorization, and give a brief description of the multilevel LU factorization. We first introduce a performance model called Hierarchical Cluster Platform (Hcp), encapsulating the characteristics ...

متن کامل

Comparison of Simulated Annealing and Electromagnetic Algorithms for Solution of Extended Portfolio Model

This paper presents two meta-heuristic algorithms to solve an extended portfolio selection model. The extended model is based on the Markowitz's Model, aiming to minimize investment risk in a specified level of return. In order to get the Markowitz model close to the real conditions, different constraints were embedded on the model which resulted in a discrete and non-convex solution space. ...

متن کامل

Linear Extended Whitening Filters

In this paper we present a class of linear whitening filters termed linear extended whitening filters (EWFs) which are whitening filters that have desirable secondary properties and can be used for simplifying algorithms, or achieving desired side-effects on given secondary matrices, random vectors or random processes. Further, we present an application of EWFs for simplification of QR decompos...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • SIAM J. Matrix Analysis Applications

دوره 35  شماره 

صفحات  -

تاریخ انتشار 2014