Volume 20, Issue 5
A Reverse Order Implicit Q-Theorem and the Arnoldi Process

Gui Zhi Chen & Zhong Xiao Jia

DOI:

J. Comp. Math., 20 (2002), pp. 519-524

Published online: 2002-10

Preview Full PDF 30 1056
Export citation
  • Abstract

Let A be a real square matrix and VTAV = G be an upper Hessenberg matrix with positive subdiagonal entries, where V is an orthogonal matrix. Then the implicit Q-theorem states that once the first column of V is given then V and G are uniquely determined too. Second, it is proved that for a Krylov subspace tewo formulations of the Arnoldi process are equivalent and in one to one correspondence. Finally, by the equivalence relation and the reverse vector sequence generated by the Arnoldi process is given, then the vector sequence and resulting Hessenberg matrix are uniquely determined.

  • Keywords

Implicit Q-theorem Reverse order implicit Q-theorem Truncated version Arnoldi process

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{JCM-20-519, author = {}, title = {A Reverse Order Implicit Q-Theorem and the Arnoldi Process}, journal = {Journal of Computational Mathematics}, year = {2002}, volume = {20}, number = {5}, pages = {519--524}, abstract = { Let A be a real square matrix and VTAV = G be an upper Hessenberg matrix with positive subdiagonal entries, where V is an orthogonal matrix. Then the implicit Q-theorem states that once the first column of V is given then V and G are uniquely determined too. Second, it is proved that for a Krylov subspace tewo formulations of the Arnoldi process are equivalent and in one to one correspondence. Finally, by the equivalence relation and the reverse vector sequence generated by the Arnoldi process is given, then the vector sequence and resulting Hessenberg matrix are uniquely determined. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8936.html} }
TY - JOUR T1 - A Reverse Order Implicit Q-Theorem and the Arnoldi Process JO - Journal of Computational Mathematics VL - 5 SP - 519 EP - 524 PY - 2002 DA - 2002/10 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8936.html KW - Implicit Q-theorem KW - Reverse order implicit Q-theorem KW - Truncated version KW - Arnoldi process AB - Let A be a real square matrix and VTAV = G be an upper Hessenberg matrix with positive subdiagonal entries, where V is an orthogonal matrix. Then the implicit Q-theorem states that once the first column of V is given then V and G are uniquely determined too. Second, it is proved that for a Krylov subspace tewo formulations of the Arnoldi process are equivalent and in one to one correspondence. Finally, by the equivalence relation and the reverse vector sequence generated by the Arnoldi process is given, then the vector sequence and resulting Hessenberg matrix are uniquely determined.
Gui Zhi Chen & Zhong Xiao Jia. (1970). A Reverse Order Implicit Q-Theorem and the Arnoldi Process. Journal of Computational Mathematics. 20 (5). 519-524. doi:
Copy to clipboard
The citation has been copied to your clipboard