Some properties of a class of band matrices

Authors:
W. D. Hoskins and P. J. Ponzo

Journal:
Math. Comp. **26** (1972), 393-400

MSC:
Primary 65F30

DOI:
https://doi.org/10.1090/S0025-5718-1972-0303703-3

MathSciNet review:
0303703

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote the band matrix, of bandwidth , with the binomial coefficients in the expansion of as the elements in each row and column. Using the fact that the rows of provide the coefficients for the th central difference, a number of properties of are obtained for all positive integers and . These include obtaining explicit formulas for and an upper triangular matrix such that is lower triangular.

**[1]**R. G. Stanton & D. A. Sprott, ``Some finite inversion formulae,''*Math. Gazette*, v. 46, 1962, pp. 197-202.**[2]**Richard S. Varga,*Matrix iterative analysis*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR**0158502****[3]***Numerical solution of ordinary and partial differential equations.*, Based on a Summer School held in Oxford, August-September 1961, Pergamon Press, Oxford-London-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1962. MR**0146969****[4]**D. E. Rutherford,*Some continuant determinants arising in physics and chemistry. II*, Proc. Roy. Soc. Edinburgh. Sect. A.**63**(1952), 232–241. MR**0059232****[5]**John Riordan,*Combinatorial identities*, John Wiley & Sons, Inc., New York-London-Sydney, 1968. MR**0231725****[6]**A. C. Aitken,*Determinants and Matrices*, Oliver & Boyd, London, 1936, p. 124.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0303703-3

Keywords:
Determinants,
band matrices,
inverse matrices,
norms on inverses

Article copyright:
© Copyright 1972
American Mathematical Society