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Abstract: In this paper a new method for computing the action of the matrix exponential on a vector , where is a complex matrix and is a positive real number, is proposed. Our approach is based on vector valued rational approximation where the approximants are determined by the denominator polynomials whose coefficients are obtained by solving an inexpensive linear least-squares problem. No matrix multiplications or divisions but matrix-vector products are required in the whole process. A technique of scaling and recurrence enables our method to be more effective when the problem is for fixed and many values of . We also give a backward error analysis in exact arithmetic for the truncation errors to derive our new algorithm. Preliminary numerical results illustrate that the new algorithm performs well. [Copyright &y& Elsevier]

Abstract: In this paper, we give an analytical model of the compression error of down-sampled compression based on wavelet transform, which explains why down-sampling before compression can improve coding performance. And we approximate the missing details due to down-sampling and compression by using the linear combination of a set of basis vectors with norm. Then we propose a down-sampled and high frequency information approximated coding scheme and apply it to natural images, and achieve gains of both subjective quality and objective quality compared with JPEG2000. [Copyright &y& Elsevier]