This paper presents the concept of perfect matrices of Lagrange differences which are used to analyze relationships between RR and JT intervals during the bicycle ergometry exercise. The concept of the perfect matrix of Lagrange differences, its parameters, the construction of the load function and the corresponding optimization problem, the introduction of internal and external smoothing, embedding of the scalar parameter time series into the phase plane—all these computational techniques allow visualization of complex dynamical processes taking place in the cardiovascular system during the load and the recovery processes. Detailed analysis is performed with one person’s RR and JT records only—but the presented techniques open new possibilities for novel interpretation of the dynamics of the cardiovascular system.

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It is well known that solutions of many ordinary differential equations allow presentation in the power series form. In the paper we introduce and analyze rigorous conditions under which the later series (solutions) can be reduced to a finite sum of standard functions. Some areas of practical applicability of the proposed algorithm are discussed.

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