A New Scaling and Squaring Algorithm for the Matrix Exponential
نویسندگان
چکیده
منابع مشابه
A New Scaling and Squaring Algorithm for the Matrix Exponential
The scaling and squaring method for the matrix exponential is based on the approximation eA ≈ (rm(2−sA))2s , where rm(x) is the [m/m] Padé approximant to ex and the integers m and s are to be chosen. Several authors have identified a weakness of existing scaling and squaring algorithms termed overscaling, in which a value of s much larger than necessary is chosen, causing a loss of accuracy in ...
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The matrix exponential plays a fundamental role in linear differential equations arising in engineering, mechanics, and control theory. The most widely used, and the most generally efficient, technique for calculating the matrix exponential is a combination of “scaling and squaring” with a Padé approximation. For alternative scaling and squaring methods based on Taylor series, we present two mo...
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The scaling and squaring method is the most widely used method for computing the matrix exponential, not least because it is the method implemented in MATLAB’s expm function. The method scales the matrix by a power of 2 to reduce the norm to order 1, computes a Padé approximant to the matrix exponential, and then repeatedly squares to undo the effect of the scaling. We give a new backward error...
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The matrix exponential plays a fundamental role in linear systems arising in engineering, mechanics and control theory. In this paper, an efficient Taylor method for computing matrix exponentials is presented. Taylor series truncation together with a modification of the PatersonStockmeyer method avoiding factorial evaluations, and the scaling-squaring technique, allow efficient computation of t...
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A popular method for computing the matrix logarithm is the inverse scaling and squaring method, which essentially carries out the steps of the scaling and squaring method for the matrix exponential in reverse order. Here we make several improvements to the method, putting its development on a par with our recent version [SIAM J. Matrix Anal. Appl., 31 (2009), pp. 970–989] of the scaling and squ...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2010
ISSN: 0895-4798,1095-7162
DOI: 10.1137/09074721x