The.Algorithm.Design.Manual.Springer-Verlag.1998
The.Algorithm.Design.Manual.Springer-Verlag.1998 The.Algorithm.Design.Manual.Springer-Verlag.1998
Matrix Multiplication Related Problems: Solving linear equations (see page ), shortest path (see page ). Next: Determinants and Permanents Up: Numerical Problems Previous: Bandwidth Reduction Algorithms Mon Jun 2 23:33:50 EDT 1997 file:///E|/BOOK/BOOK3/NODE138.HTM (4 of 4) [19/1/2003 1:30:18]
Determinants and Permanents Next: Constrained and Unconstrained Optimization Up: Numerical Problems Previous: Matrix Multiplication Determinants and Permanents Input description: An matrix M. Problem description: What is the determinant |M| or the permanent perm(M) of the matrix m? Discussion: Determinants of matrices provide a clean and useful abstraction in linear algebra that can used to solve a variety of problems: ● Testing whether a matrix is singular, meaning that the matrix does not have an inverse. A matrix M is singular iff |M| = 0. ● Testing whether a set of d points lies on a plane in fewer than d dimensions. If so, the system of equations they define is singular, so |M| = 0. ● Testing whether a point lies to the left or right of a line or plane. This problem reduces to testing whether the sign of a determinant is positive or negative, as discussed in Section . ● Computing the area or volume of a triangle, tetrahedron, or other simplicial complex. These quantities are a function of the magnitude of the determinant, as discussed in Section . file:///E|/BOOK/BOOK3/NODE139.HTM (1 of 3) [19/1/2003 1:30:19]
- Page 335 and 336: Approximation Algorithms Next: Appr
- Page 337 and 338: Approximating Vertex Cover Next: Th
- Page 339 and 340: The Euclidean Traveling Salesman Ne
- Page 341 and 342: The Euclidean Traveling Salesman Ne
- Page 343 and 344: Exercises 1. Prove that the low deg
- Page 345 and 346: Data Structures Next: Dictionaries
- Page 347 and 348: Dictionaries Next: Priority Queues
- Page 349 and 350: Dictionaries use a function that ma
- Page 351 and 352: Dictionaries Implementation-oriente
- Page 353 and 354: Priority Queues ● Besides access
- Page 355 and 356: Priority Queues Fibonacci heaps [FT
- Page 357 and 358: Suffix Trees and Arrays Figure: A t
- Page 359 and 360: Suffix Trees and Arrays [GBY91]. Se
- Page 361 and 362: Graph Data Structures algorithms).
- Page 363 and 364: Graph Data Structures including the
- Page 365 and 366: Set Data Structures Next: Kd-Trees
- Page 367 and 368: Set Data Structures parent pointers
- Page 369 and 370: Kd-Trees Next: Numerical Problems U
- Page 371 and 372: Kd-Trees about p. Say we are lookin
- Page 373 and 374: Numerical Problems Next: Solving Li
- Page 375 and 376: Numerical Problems Mon Jun 2 23:33:
- Page 377 and 378: Solving Linear Equations algorithm
- Page 379 and 380: Solving Linear Equations Matrix inv
- Page 381 and 382: Bandwidth Reduction images near eac
- Page 383 and 384: Matrix Multiplication Next: Determi
- Page 385: Matrix Multiplication The linear al
- Page 389 and 390: Determinants and Permanents exposit
- Page 391 and 392: Constrained and Unconstrained Optim
- Page 393 and 394: Constrained and Unconstrained Optim
- Page 395 and 396: Linear Programming variable assignm
- Page 397 and 398: Linear Programming The book [MW93]
- Page 399 and 400: Random Number Generation Next: Fact
- Page 401 and 402: Random Number Generation is largely
- Page 403 and 404: Random Number Generation Related Pr
- Page 405 and 406: Factoring and Primality Testing The
- Page 407 and 408: Factoring and Primality Testing Alg
- Page 409 and 410: Arbitrary-Precision Arithmetic If y
- Page 411 and 412: Arbitrary-Precision Arithmetic PARI
- Page 413 and 414: Knapsack Problem Next: Discrete Fou
- Page 415 and 416: Knapsack Problem is a subset of S'
- Page 417 and 418: Discrete Fourier Transform Next: Co
- Page 419 and 420: Discrete Fourier Transform an algor
- Page 421 and 422: Combinatorial Problems Next: Sortin
- Page 423 and 424: Sorting Next: Searching Up: Combina
- Page 425 and 426: Sorting The simplest approach to ex
- Page 427 and 428: Sorting operations, implying an sor
- Page 429 and 430: Searching large performance improve
- Page 431 and 432: Searching Notes: Mehlhorn and Tsaka
- Page 433 and 434: Median and Selection followed by fi
- Page 435 and 436: Generating Permutations Next: Gener
Matrix Multiplication<br />
Related Problems: Solving linear equations (see page ), shortest path (see page ).<br />
Next: Determinants and Permanents Up: Numerical Problems Previous: Bandwidth Reduction<br />
<strong>Algorithm</strong>s<br />
Mon Jun 2 23:33:50 EDT 1997<br />
file:///E|/BOOK/BOOK3/NODE138.HTM (4 of 4) [19/1/2003 1:30:18]
Change language