INVERTING CIRCULANT MATRICES

被引:25
作者
SEARLE, SR
机构
[1] Biometrics Unit Cornell University Ithaca
关键词
D O I
10.1016/0024-3795(79)90007-7
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The elements of the inverse of a circulant matrix having only three non-zero elements in each row (located in cyclically adjacent columns) are derived analytically from the solution of a recurrence equation. Expressing any circulant as a product containing these three-element-type circulants then provides an algorithm for inverting circulants in general. Extension is also made to deriving generalized inverses of certain singular circulants. © 1979.
引用
收藏
页码:77 / 89
页数:13
相关论文
共 11 条
[1]   CALCULATION OF ANALYTIC FUNCTIONS OF CYCLIC MATRICES [J].
ABRAHAM, PB ;
WEISS, G .
JOURNAL OF MATHEMATICAL PHYSICS, 1962, 3 (02) :340-&
[2]   DESIGNS WITH PARTIAL FACTORIAL BALANCE [J].
ANDERSON, DA .
ANNALS OF MATHEMATICAL STATISTICS, 1972, 43 (04) :1333-&
[3]   INVERSION OF CYCLIC MATRICES [J].
CALAIS, JL ;
APPEL, K .
JOURNAL OF MATHEMATICAL PHYSICS, 1964, 5 (08) :1001-&
[4]  
Duncan WJ, 1944, PHILOS MAG, V35, P660
[5]   INVERSE OVERLAP MATRIX FOR PERIODIC ARRAYS OF ATOMS [J].
GILBERT, TL .
JOURNAL OF MATHEMATICAL PHYSICS, 1962, 3 (01) :107-&
[6]   AN INVERSION TECHNIQUE FOR CERTAIN PATTERNED MATRICES [J].
KOUNIAS, EG .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1968, 21 (03) :695-&
[7]   ON THE CALCULATION OF THE INVERSE OF THE OVERLAP MATRIX IN CYCLIC SYSTEMS [J].
LOWDIN, PO ;
PAUNCZ, R ;
DEHEER, J .
JOURNAL OF MATHEMATICAL PHYSICS, 1960, 1 (06) :461-467
[8]   TESTING AND ESTIMATION FOR A CIRCULAR STATIONARY MODEL [J].
OLKIN, I ;
PRESS, SJ .
ANNALS OF MATHEMATICAL STATISTICS, 1969, 40 (04) :1358-+
[9]  
Paige C. C., 1975, Journal of Statistical Computation and Simulation, V4, P173, DOI 10.1080/00949657508810122
[10]  
Penrose R., 1955, P CAMB PHIL SOC, V51, P406, DOI [10.1017/S0305004100030401, DOI 10.1017/S0305004100030401]