Algorithm 406: exact solution of linear equations using residue arithmetic [F4]

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Algorithm 406: exact solution of linear equations using residue arithmetic [F4]

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Communications of the ACM archive
Volume 14 , Issue 3 (March 1971) table of contents

Pages: 180 - 184

Year of Publication: 1971

ISSN:0001-0782

Author

Jo Ann Howell

Univ. of Texas at Austin, TX

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 5, Downloads (12 Months): 24, Citation Count: 2

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appendices and supplements references cited by index terms collaborative colleagues

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exact solution of linear system by residue arithmetic

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	Howell, J. A. and Gregory, R.T. An algorithm for solving linear algebraic equations using residue arithmetic I. BIT 9, 3 (1969), 200--224.
	2	Howell, J. A. and Gregory, R.T. An algorithm for solving linear algebraic equations using residue arithmetic II. BIT 9, 4 (1969), 324-337.
	3	Howell, J. A. and Gregory, R.T. Solving linear equations using residue arithmetic-algorithm II. BIT 10, 1 (1970), 23-37.
	4	Lotkin, M. A set of test matrices. MTAC 9 (1955), 153-161.
	5	Borosh, I. and Fraenkel, A.S. Exact solutions of linear equations with rational coefficients by congruence techniques. Math. Comp. 20 (1966), 107-112.
	6	Newman, M. Solving equations exactly, J. Research NBS 17B, 4 (1967), 171-179.
	7	Takahasi, H. and Ishibashi, Y. A new method for exact calculations by a digital computer. Information Processing in Japan 1, (1961), 28-42.
	8	Donald E. Knuth, The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms, Addison-Wesley Longman Publishing Co., Inc., Boston, MA, 1997

CITED BY 2

	S. Cabay , T. P. L. Lam, Congruence Techniques for the Exact Solution of Integer Systems of Linear Equations, ACM Transactions on Mathematical Software (TOMS), v.3 n.4, p.386-397, Dec. 1977
	Jörn Springer, Exact solution of general integer systems of linear equations, ACM Transactions on Mathematical Software (TOMS), v.12 n.1, p.51-61, March 1986

INDEX TERMS

Keywords:
Gaussian elimination, adjoint matrix, determinant, ill-condition, linear equations, matrix inversion, mixed-radix conversion, mixed-radix representation, modulus, prime number, residue arithmetic, symmetric mixed-radix representation, symmetric residue

Collaborative Colleagues:

Jo Ann Howell: colleagues

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