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. (1368). AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX. , 1(2), -.
. "AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX". , 1, 2, 1368, -.
. (1368). 'AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX', , 1(2), pp. -.
. AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX. , 1368; 1(2): -.

AN ALGORITHM FOR FINDING THE EIGENPAIRS OF A SYMMETRIC MATRIX

Journal of Sciences, Islamic Republic of Iran
مقاله 13، دوره 1، شماره 2، خرداد 1990    اصل مقاله (269.7 K)
چکیده
The purpose of this paper is to show that ideas and techniques of the
homotopy continuation method can be used to find the complete set of
eigenpairs of a symmetric matrix. The homotopy defined by Chow, Mallet-
Paret and York [I] may be used to solve this problem with 2""-n curves
diverging to infinity which for large n causes a great inefficiency. M. Chu 121
introduced a homotopy equation to solve this problem, In this method it is
necessary to follow 2n curves to handle the problem. Our method is basedon
a special homotopy system of equations which consists of exactly n distinct
smooth curves and connects trivial soiution to desired eigenpairs. It is
important that in our method we avoidfindingexplicitlythecoefficient of the
characteristic equation, as all experienced practitioners are aware of the
large error that may result from the use of the approximate coefficientsof the
characteristic polynomial
عنوان مقاله [English]
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چکیده [English]
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