Calculating a function of a matrix with a real spectrum

0547353 - ÚFCH JH 2023 RIV NL eng J - Journal Article
Kubelík, Petr - Kurbatov, V. G. - Kurbatova, I. V.
Calculating a function of a matrix with a real spectrum.
Numerical Algorithms. Roč. 90, č. 3 (2022), s. 905-930. ISSN 1017-1398. E-ISSN 1572-9265
R&D Projects: GA ČR(CZ) GC20-10591J
Institutional support: RVO:61388955
Keywords : approximation * algorithm * compute * gamma * logarithm * integrals * cosine * Matrix function * Polynomial interpolation * Divided differences * Reordering * Multiprecision arithmetic * Schur-Parlett algorithm
OECD category: Physical chemistry
Impact factor: 2.1, year: 2022
Method of publishing: Limited access

Let T be a square matrix with a real spectrum, and let f be an analytic function. The problem of the approximate calculation of f(T) is discussed. Applying the Schur triangular decomposition and the reordering, one can assume that T is triangular and its diagonal entries t(ii) are arranged in increasing order. To avoid calculations using the differences t(ii) t(jj) with close (including equal) t(ii) and t(jj), it is proposed to represent T in a block form and calculate the two main block diagonals using interpolating polynomials. The rest of the f(T) entries can be calculated using the Parlett recurrence algorithm. It is also proposed to perform some scalar operations (such as the building of interpolating polynomials) with an enlarged number of significant decimal digits.
Permanent Link: http://hdl.handle.net/11104/0323595