### Matrix computations and mathematical software

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Computation of eigenvalues and eigenvectors. Given a matrix , compute scalars or and vectors or such that.

Providing estimates for the condition number of a matrix , i. The computation of the rank of a matrix, i. Generalized eigenvalue problems, i. Singular value decomposition , i. There are presently many software packages for linear algebra problems. Some are interactive, others are not. Symbolic packages are usually interactive and allow also the numerical treatment of small scale problems. Their main field of application is in algorithms with high numerical robustness and large scale computations. They provide. Commands to perform low-level linear algebra manipulations such as adding a multiple of a vector to another vector, computing an inner product, etc.

Routines to generate matrices with pseudo-random entries and special types of matrices, such as the Bezout or Sylvester matrix, Jacobian, Wronskian and Hessian matrices. Symbolic and numeric routines to solve the fundamental and related problems for dense matrices and some sparse matrices with special structure, in particular band matrices.

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The routines are based on direct methods or for eigenvalue problems very robust and well-understood iterative methods such as the QR-algorithm. The leading package of non-interactive, numerical routines for linear algebra computations is LAPACK [a1] , which is freely available from the electronic numerical analysis library netlib, [a8].

The BLAS are also available from netlib. They perform the low-level linear algebra routines; highly efficient implementations are available for current machines and regularly updated.

The routines in LAPACK are available in specific forms for general dense, band and symmetric matrices and for various variable types real, double precision real, complex, double precision complex. However, there are several other packages that can either solve linear systems with sparse matrices or compute eigenvalues of sparse matrices or both. Linear systems are either solved by direct sparse methods or by iterative methods.

A survey of freely available software is at present maintained at the [a6]. Note that realistic applications of such matrices, i. For the underlying numerical analysis ideas, see [a4]. Important features are:. The user decides how many eigenvalues are wanted and has a choice of possibilities to decide which ones, e. The package is independent of the storage structure of the matrices. Computation of eigenvalues and eigenvectors.

## Linear algebra software packages

Given a matrix , compute scalars or and vectors or such that. Providing estimates for the condition number of a matrix , i. The computation of the rank of a matrix, i. Generalized eigenvalue problems, i. Singular value decomposition , i.

There are presently many software packages for linear algebra problems. Some are interactive, others are not. Symbolic packages are usually interactive and allow also the numerical treatment of small scale problems. Their main field of application is in algorithms with high numerical robustness and large scale computations. They provide. Commands to perform low-level linear algebra manipulations such as adding a multiple of a vector to another vector, computing an inner product, etc.

Routines to generate matrices with pseudo-random entries and special types of matrices, such as the Bezout or Sylvester matrix, Jacobian, Wronskian and Hessian matrices. Symbolic and numeric routines to solve the fundamental and related problems for dense matrices and some sparse matrices with special structure, in particular band matrices. The routines are based on direct methods or for eigenvalue problems very robust and well-understood iterative methods such as the QR-algorithm. The leading package of non-interactive, numerical routines for linear algebra computations is LAPACK [a1] , which is freely available from the electronic numerical analysis library netlib, [a8].

## Mathematical Software at UCLA-Mathnet | UCLA Department of Mathematics

The BLAS are also available from netlib. They perform the low-level linear algebra routines; highly efficient implementations are available for current machines and regularly updated. The routines in LAPACK are available in specific forms for general dense, band and symmetric matrices and for various variable types real, double precision real, complex, double precision complex.

However, there are several other packages that can either solve linear systems with sparse matrices or compute eigenvalues of sparse matrices or both. Linear systems are either solved by direct sparse methods or by iterative methods.

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A survey of freely available software is at present maintained at the [a6]. Note that realistic applications of such matrices, i. For the underlying numerical analysis ideas, see [a4]. Important features are:. The user decides how many eigenvalues are wanted and has a choice of possibilities to decide which ones, e. The package is independent of the storage structure of the matrices. Toggle Main Navigation. Books Books MathWorks. Search MathWorks. Matrix Computations, 4e Written for scientists and engineers, Matrix Computations provides comprehensive coverage of numerical linear algebra.

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