The Use of Semi Inherited LU Factorization of Matrices in Interpolation of Data

الموضوعات :

محمدعلی فریبرزی عراقی ¹ (Department of mathematics, Islamic Azad University,Central Tehran Branch, Tehran, Iran)
امیر فلاح زاده ² (Department of mathematics, Islamic Azad University,Central Tehran Branch, Tehran, Iran)

تاريخ الإرسال : 04 الخميس , محرم, 1430 تاريخ التأكيد : 07 الأربعاء , ربيع الأول, 1430 تاريخ الإصدار : 08 الأربعاء , رجب, 1430

الکلمات المفتاحية: Semi Inherited LU factorization, Interpolation matrix, Semi inherited interpola‌tion,

ملخص المقالة :

The polynomial interpolation in one dimensional space R is an important method to approximate the functions. The Lagrange and Newton methods are two well known types of interpolations. In this work, we describe the semi inherited interpolation for approximating the values of a function. In this case, the interpolation matrix has the semi inherited LU factorization.

المصادر:

[1] Arav, M., Bevis, J. and Hall, F. J., Inherited LU-factorization of matrices, Linear Algebra, and it's Application 427, 16-41, 2007.

[2] Cheney, W., and Light, W., A course in approximation theory, Brooks/Cole  Pub­lishing Company, Pacific Grove, California, 2000.

[3] Demmel, J. W., Applied Numerical Linear Algebra, SIAM, Society for Industrial and Applied Mathematics, 1997.

[4] Gill, P. E., Murray, W., and Wright, M. H., Numerical Linear Algebra and Optimiza­tion, Addison-Wesley Publishing Company, Redwood City, California, 1991.

 [5] Johnson, C. R., Olesky, D. D. and Van den Driessche, P., Inherited  matrix entries:  LU factorization,  SIAM  J. Matrix Anal. Appl, 10, 97-104, 1989.

 [6] Lay, D. C., Linear Algebra and Its Applications, Third Edition, Addison Wesley, Boston, 2003.

[7] Powell, M. J. D., Approximation theory and methods, Cambridge University Press, 1996.

[8] Rivlin, T. J., An Introduction to the Approximation of Functions, Blaisdell Pub­lishing Company, Waltham, 1969.