In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; andmethods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.As a result, the book represents a blend of new methods in general computational analysis,and specific, but also generic, techniques for study of systems theory ant its particularbranches, such as optimal filtering and information compression.- Best operator approximation,- Non-Lagrange interpolation,- Generic Karhunen-Loeve transform- Generalised low-rank matrix approximation- Optimal data compression- Optimal nonlinear filtering

本書は、非線形システムの深奥に潜む「因果」を、演算子近似という数理言語で解き明かす知の結晶です。カジェロが提示する理論は、混沌の中に秩序を見出す哲学的探究であり、情報の「本質」を濾過しようとするストイックな知性が、読者を思考の極北へと誘います。 映像化作品では、この抽象的な数理の美学がダイナミックな視覚体験へと昇華されています。テキストが湛える沈黙の深みと、映像が補完する動的な躍動感。この両メディアを往復することで、数式が秘める生命力と世界の真理を、より情熱的に体感できるはずです。理性の極致が生む驚異のドラマを、ぜひ味わってください。