Black box methods for least squares problems

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Black box methods for least squares problems

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 2001 international symposium on Symbolic and algebraic computation table of contents

London, Ontario, Canada

Pages: 297 - 302

Year of Publication: 2001

ISBN:1-58113-417-7

Author

B. D. Saunders

Univ. of Delaware, Newark

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 0, Downloads (12 Months): 24, Citation Count: 2

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ABSTRACT

We present algorithms to construct an efficient black box for the pseudoinverse, A^t, of a black box matrix A. This in also known as the Moore-Penrose inverse of A. For the system Ax = b over a subfield of the complex numbers: the vector x = A^tb is the least squares solution having the least norm. When we say that A is a black box matrix we mean simply that methods are given to compute the matrix-vector products Au and u^TA, for vectors u and vectors v of compatible length. No other assumptions are made about the structure or representation of the matrix.

The entries may be integers or rational numbers or elements of a finite field. For the integer or rational case the method uses homomorphic images, and is based on an algorithm capable of computing the black box for the pseudoinverse, when it exists, over an arbitrary field. We discuss the asymptotic costs and some variants that are likely to be useful in practice.

Over a finite field the solution, x = A^tb, is uniquely defined when it exists. The ability to produce this particular solution is a useful addition to the range of ways solution to singular linear systems may be offered in the black box model.

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.

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CITED BY 2

	Qi Zhu , Shaohua Tan , Ying Qiao, A robust high-order recursive quadratic algorithm for linear-in-the-parameters models, Proceedings of the 17th IASTED international conference on Modelling and simulation, p.476-481, May 24-26, 2006, Montreal, Canada
	Aude Rondepierre , Jean-Guillaume Dumas, Algorithms for symbolic/numeric control of affine dynamical systems, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.277-284, July 24-27, 2005, Beijing, China