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 ALAMT  Vol.4 No.2 , June 2014
Generalized Inversions of Hadamard and Tensor Products for Matrices
Abstract: We shall give natural generalized solutions of Hadamard and tensor products equations for matrices by the concept of the Tikhonov regularization combined with the theory of reproducing kernels.
Cite this paper: Saitoh, S. (2014) Generalized Inversions of Hadamard and Tensor Products for Matrices. Advances in Linear Algebra & Matrix Theory, 4, 87-95. doi: 10.4236/alamt.2014.42006.
References

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[9]   Yamada, A. (2012) Oppenheim’s Inequality and RKHS. Mathematical Inequalities and Applications, 15, 449-456.

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[12]   Castro, L.P., Fujiwara, H., Saitoh, S., Sawano, Y., Yamada, A. and Yamada, M. (2012) Fundamental Error Estimates Inequalities for the Tikhonov Regularization Using Rreproducing Kernels. International Series of Numerical Mathematics 161, Inequalities and Appications 2010, Springer, Basel, 87-101.

[13]   Castro, L.P., Saitoh, S., Sawano, Y. and Silva, A.S. (2012) Discrete Linear Differential Equations. Analysis, 32, 181- 191.
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[14]   Castro, L.P., Fujiwara, H., Rodrigues, M. M., Saitoh, S. and Tuan, V.K. (2014) Aveiro Discretization Method in Mathematics: A New Discretization Principle. In: Pardalos, P. and Rassias, T.M., Eds., Mathematics without Boundaries: Surveys in Pure Mathematics, in press.

[15]   Castro, L.P., Fujiwara, H., Qian, T. and Saitoh, S. (2014) How to Catch Smoothing Properties and Analyticity of Functions by Computers? In: Pardalos, P. and Rassias, T.M., Eds., Mathematics without Boundaries: Surveys in Interdisipinary Research, in press.

[16]   Castro, L. P., Saitoh, S. and Yamada, A. (2014) Representations of Solutions of Tichhonov Functional Equations and Applications to Multiplication Operators of the Szego Spaces (submitted).

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[18]   Kuroda, T., Michiwaki, H., Saitoh, S. and Yamane, M. (2014) New Meanings of the Division by Zero and Interpretations on 100/0 = 0 and on 0/0 = 0. International Journal of Applied Mathematics, 27, 191-198.

 
 
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