Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On solving symmetric systems of linear equations in an unnormalized
  Krylov subspace framework   In an unnormalized Krylov subspace framework for solving symmetric systems of
linear equations, the orthogonal vectors that are generated by a Lanczos
process are not necessarily on the form of gradients. Associating each
orthogonal vector with a triple, and using only the three-term recurrences of
the triples, we give conditions on whether a symmetric system of linear
equations is compatible or incompatible. In the compatible case, a solution is
given and in the incompatible case, a certificate of incompatibility is
obtained. In particular, the case when the matrix is singular is handled.
  We also derive a minimum-residual method based on this framework and show how
the iterates may be updated explicitly based on the triples, and in the
incompatible case a minimum-residual solution of minimum Euclidean norm is
obtained.

23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org