Bibliothèque de L'IMIST/CNRST

Includes bibliographical references (p. 276-327) and index.

Cover13; -- Singular and Degenerate Cauchy Problems -- Copyright Page -- Contents -- Preface -- Chapter 1. Singular Partial Differential Equations of EPD Type -- 1.1. Examples -- 1.2. Mean values in Rn -- 1.3. The Fourier method -- 1.4. Connection formulas and properties of solutions for EPD equations in D' and S' -- 1.5. Spectral techniques and energy methods in Hilbert space -- 1.6. EPD equations in general spaces -- 1.7. Transmutation -- Chapter 2. Canonical Sequences of Singular Cauchy Problems -- 2.1. The rank one situation -- 2.2. Resolvants -- 2.3. Examples with m2945; = 0 -- 2.4. Expressions for general resolvants -- 2.5. The Euclidean case plus generalizations -- Chapter 3. Degenerate Equations with Operator Coefficients -- 3.1. Introduction -- 3.2. The Cauchy problem by spectral techniques -- 3.3. Strongly regular equations -- 3.4. Weakly regular equations -- 3.5. Linear degenerate equations -- 3.6. Semilinear degenerate equations -- 3.7. Doubly nonlinear equations -- Chapter 4. Selected Topics -- 4.1. Introduction -- 4.2. Huygens' principle -- 4.3. The generalized radiation problem of Weinstein -- 4.4. Improperly posed problems -- 4.5. Miscellaneous problems -- REFERENCES -- INDEX.

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;<BR id="CRLF">methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and<BR id="CRLF">methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory.<BR id="CRLF"><BR id="CRLF">As a result, the book represents a blend of new methods in general computational analysis, <BR id="CRLF">and specific, but also generic, techniques for study of systems theory ant its particular<BR id="CRLF">branches, such as optimal filtering and information compression.

Description based on print version record.