Tutorial by Examples: composition

Hereby a matrix will be decomposed into an upper trangular and an lower triangular matrix. Often it will be used to increase the performance and stability (if it's done with permutation) of Gauß elimination. However, quite often does this method not or badly work as it is not stable. For example A...

Two useful higher-order functions are the binary application (@@) and reverse-application or "pipe" (|>) operators. Although since 4.01 they're available as primitives, it might still be instructive to define them here: let (|>) x f = f x let (@@) f x = f x Consider the problem ...

If A is a complex and quadratic matrix there exists a unitary Q such that Q*AQ = T = D + N with D being the diagonal matrix consisting of the eigenvalues and N being strictly upper tridiagonal. A = [3 6 1 23 13 1 0 3 4]; T = schur(A); We also display the runtime of schur dependent on ...

Given an m times n matrix A with n larger than m. The singular value decomposition [U,S,V] = svd(A); computes the matrices U,S,V. The matrix U consists of the left singular eigenvectors which are the eigenvectors of A*A.' while V consists of the right singular eigenvalues which are the eigenvec...

C++ & Java are both object-oriented languages, thus the following diagram applies to both.