Symmetric tensors and symmetric tensor rank

... For example, a 3-way array Jaijk K ∈ Cn×n×n is symmetric if aijk = aikj = ajik = ajki = akij = akji for all i, j, k ∈ {1, . . . , n}. Such arrays have been improperly labeled ‘supersymmetric’ tensors (cf. [10, 34, 45] among others); this terminology should be avoided since it refers to an entirely d ...

... For example, a 3-way array Jaijk K ∈ Cn×n×n is symmetric if aijk = aikj = ajik = ajki = akij = akji for all i, j, k ∈ {1, . . . , n}. Such arrays have been improperly labeled ‘supersymmetric’ tensors (cf. [10, 34, 45] among others); this terminology should be avoided since it refers to an entirely d ...

Regularization of Least Squares Problems

... Back in 1923 Hadamard introduced the concept of well-posed and ill-posed problems. A problem is well-posed, if — it is solvable — its solution is unique — its solution depends continuously on system parameters (i.e. arbitrary small perturbation of the data can not cause arbitrary large perturbation ...

... Back in 1923 Hadamard introduced the concept of well-posed and ill-posed problems. A problem is well-posed, if — it is solvable — its solution is unique — its solution depends continuously on system parameters (i.e. arbitrary small perturbation of the data can not cause arbitrary large perturbation ...

differential equations and linear algebra manual

... Solution (a) Since this equation solves a sin y term, it is not linear in y. (b) and (c) Since these equations have no nonlinear terms in y, they are linear. 11 The product rule gives what derivative for et e−t ? This function is constant. At t = 0 this constant is 1. Then et e−t = 1 for all t. Solu ...

... Solution (a) Since this equation solves a sin y term, it is not linear in y. (b) and (c) Since these equations have no nonlinear terms in y, they are linear. 11 The product rule gives what derivative for et e−t ? This function is constant. At t = 0 this constant is 1. Then et e−t = 1 for all t. Solu ...

Graph Theory Definitions - Cornell Computer Science

... There are several things going on here. First of all, note that the seen[] array has been replaced by the colour[] array. We also have an extra parameter to dfs() the parent of u in the DFS tree. Now look at the first and last lines of dfs(). White vertices are those we haven' t visited yet. Any v ...

... There are several things going on here. First of all, note that the seen[] array has been replaced by the colour[] array. We also have an extra parameter to dfs() the parent of u in the DFS tree. Now look at the first and last lines of dfs(). White vertices are those we haven' t visited yet. Any v ...

An exponential-related function for decision-making in

... to consider opinions from three sides to arrive at the preferred one. (3) All the fuzzy numbers in the IFS theory can all be used to represent vagueness of “agreement”, although, they cannot be used to depict the “disagreement” of the DMs. As a mathematical tool, the IFS has demonstrated the ability ...

... to consider opinions from three sides to arrive at the preferred one. (3) All the fuzzy numbers in the IFS theory can all be used to represent vagueness of “agreement”, although, they cannot be used to depict the “disagreement” of the DMs. As a mathematical tool, the IFS has demonstrated the ability ...