Searched for: subject%3A%22induced%255C%2Bdimension%255C%2Breduction%22
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Astudillo Rengifo, R.A. (author), de Gier, J.M. (author), van Gijzen, M.B. (author)The Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a shortrecurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the...journal article 2019
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Astudillo Rengifo, R.A. (author)In several applications in science and engineering, different types of matrix problems emerge from the discretization of partial differential equations.<br/>This thesis is devoted to the development of new algorithms to solve this<br/>kind of problems. In particular, when the matrices involved are sparse and<br/>nonsymmetric. The new algorithms...doctoral thesis 2018
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Baumann, M.M. (author), Astudillo Rengifo, R.A. (author), Qiu, Y. (author), Ang, Y.M.E. (author), van Gijzen, M.B. (author), Plessix, R.E. (author)In this work, we present a new numerical framework for the efficient solution of the timeharmonic elastic wave equation at multiple frequencies. We show that multiple frequencies (and multiple righthand sides) can be incorporated when the discretized problem is written as a matrix equation. This matrix equation can be solved efficiently...journal article 2018
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Astudillo, R. (author), Van Gijzen, M.B. (author)This paper discusses the solution of largescale linear matrix equations using the Induced Dimension reduction method (IDR(s)). IDR(s) was originally presented to solve system of linear equations, and is based on the IDR(s) theorem. We generalize the IDR(s) theorem to solve linear problems in any finitedimensional space. This generalization...report 2015
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Astudillo, R. (author), Van Gijzen, M.B. (author)A new algorithm to compute eigenpairs of large unsymmetric matrices is presented. Using the Induced Dimension Reduction method (IDR), which was originally proposed for solving linear systems, we obtain a Hessenberg decomposition from which we approximate the eigenvalues and eigenvectors of a matrix. This decomposition has two main advantages....report 2014
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 Baumann, M. (author), Van Gijzen, M.B. (author) report 2014
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Astudillo, R. (author), Van Gijzen, M.B. (author)This work presents an algorithm to approximate eigenpairs of large, sparse and nonsymmetric matrices based on the Induced Dimension Reduction method (IDR(s)) introduced in [1]. We obtain a Hessenberg relation from IDR(s) computations and in conjunction with Implicitly Restarting and shiftandinvert techniques [2] we created a short recurrence...conference paper 2013
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Sleijpen, G.L.G. (author), Van Gijzen, M.B. (author)IDR(s) [P. Sonneveld and M. B. van Gijzen, SIAM J. Sci. Comput., 31 (2008), pp. 1035–1062] and BiCGstab(?) [G. L. G. Sleijpen and D. R. Fokkema, Electron. Trans. Numer. Anal., 1 (1993), pp. 11–32] are two of the most efficient shortrecurrence iterative methods for solving large nonsymmetric linear systems of equations. Which of the two is best...journal article 2010
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