Hierarchical Matrices: Algorithms and Analysis (Springer by Wolfgang Hackbusch

By Wolfgang Hackbusch

This self-contained monograph offers matrix algorithms and their research. the recent process allows not just the answer of linear structures but additionally the approximation of matrix services, e.g., the matrix exponential. different purposes contain the answer of matrix equations, e.g., the Lyapunov or Riccati equation. the mandatory mathematical history are available within the appendix.

The numerical therapy of absolutely populated large-scale matrices is generally relatively expensive. although, the means of hierarchical matrices makes it attainable to shop matrices and to accomplish matrix operations nearly with nearly linear expense and a controllable measure of approximation errors. For very important sessions of matrices, the computational fee raises basically logarithmically with the approximation errors. The operations supplied contain the matrix inversion and LU decomposition.

Since large-scale linear algebra difficulties are regular in clinical computing, the topic of hierarchical matrices is of curiosity to scientists in computational arithmetic, physics, chemistry and engineering.

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