Projection Methods for Solving Sparse Linear Systems | Zendy

R. P. Tewarson | Zendy

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Projection Methods for Solving Sparse Linear Systems

Author(s) -

R. P. Tewarson

Publication year - 1969

Publication title -

the computer journal

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.319

H-Index - 64

eISSN - 1460-2067

pISSN - 0010-4620

DOI - 10.1093/comjnl/12.1.77

Subject(s) - row , row and column spaces , diagonal , coefficient matrix , mathematics , linear system , column (typography) , permutation (music) , matrix (chemical analysis) , linear equation , system of linear equations , incidence matrix , permutation matrix , block matrix , projection (relational algebra) , graph , combinatorics , sparse matrix , block (permutation group theory) , set (abstract data type) , algorithm , computer science , geometry , mathematical analysis , materials science , database , node (physics) , structural engineering , acoustics , engineering , composite material , quantum mechanics , gaussian , programming language , eigenvalues and eigenvectors , physics , connection (principal bundle) , circulant matrix

Some methods of successive approximation for the solution of simultaneous linear equations are discussed. The coefficient matrix A of the linear system is assumed to be sparse. It is shown that savings in the computer storage and the computing time are possible, if there exists a subset of the rows (columns) of A, consisting of only orthogonal rows (columns). Such savings are also possible, if for some permutation matrices P and Q, PAQ has a particular structure, viz., singly bordered block diagonal form. It is shown that the set of orthogonal rows (columns) of A, as well as P and Q can be determined by using some results from graph theory (e.g., incidence matrices, row and column graphs, points of attachment). Geometrical interpretations of the methods and their inter-relatiohip are given.

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