Wa_english_title: "Sparse Linear Systems", Wa_emt_org: "emtorganizationalstructure:satgsoftwareandadvancedtechnologygroup", Wa_curated: "curated:donotuseinexternalfilters/productdocumentation", Wa_emtorganizationalstructure: "emtorganizationalstructure:satgsoftwareandadvancedtechnologygroup", Wa_rsoftware: "rsoftware:inteloneapitoolkits/inteloneapibasetoolkit,rsoftware:componentsproducts/inteloneapimathkernellibrary", Wa_emtcontenttype: "emtcontenttype:designanddevelopmentreference/developerguide/developerreferenceguide", Wa_emtprogramminglanguage: "emtprogramminglanguage:cc", In fact, for sparse matrices, the solution time can be predicted based on the number of non-zero elements in the array A. This approach makes the time required to solve a systems of linear equations relatively predictable, based on the size of the matrix. Consequently, if an application involves well-conditioned matrices iterative solvers can be very efficient.ĭirect Solvers, on the other hand, factor the matrix A into the product of two triangular matrices and then perform a forward and backward triangular solve. However, for well-conditioned matrices it is possible for iterative solvers to converge to a solution very quickly. In fact, for ill-conditioned matrices, the iterative process will not converge to a solution at all. Consequently, it is not possible to predict how long it will take for an iterative solver to produce a solution. The main drawback to iterative solvers is that the rate of convergence depends greatly on the values in the matrix A. This process is repeated until the difference between the approximation and the true result is sufficiently small. Based on the difference, an iterative solver calculates a new approximation that is closer to the true result than the initial approximation. Iterative Solvers start with an initial approximation to a solution and attempt to estimate the difference between the approximation and the true result. Solvers are usually classified into two groups - direct and iterative. A solver designed to work specifically on sparse systems of equations is called a sparse solver.
#Solution vectors for sparse linear equation systems software#
Generally speaking, computer software that finds solutions to systems of linear equations is called a solver. The more an algorithm can exploit the sparsity without sacrificing the correctness, the better the algorithm. For sparse matrices, computing the solution to the equation Ax = b can be made much more efficient with respect to both storage and computation time, if the sparsity of the matrix can be exploited. Conversely, matrices with very few zero elements are called dense. In many real-life applications, most of the elements in A are zero. P?lacgv p?max1 pilaver pmpcol pmpim2 ?combamax1 p?sum1 p?dbtrsv p?dttrsv p?gebal p?gebd2 p?gehd2 p?gelq2 p?geql2 p?geqr2 p?gerq2 p?getf2 p?labrd p?lacon p?laconsb p?lacp2 p?lacp3 p?lacpy p?laevswp p?lahrd p?laiect p?lamve p?lange p?lanhs p?lansy, p?lanhe p?lantr p?lapiv p?lapv2 p?laqge p?laqr0 p?laqr1 p?laqr2 p?laqr3 p?laqr5 p?laqsy p?lared1d p?lared2d p?larf p?larfb p?larfc p?larfg p?larft p?larz p?larzb p?larzc p?larzt p?lascl p?lase2 p?laset p?lasmsub p?lasrt p?lassq p?laswp p?latra p?latrd p?latrs p?latrz p?lauu2 p?lauum p?lawil p?org2l/p?ung2l p?org2r/p?ung2r p?orgl2/p?ungl2 p?orgr2/p?ungr2 p?orm2l/p?unm2l p?orm2r/p?unm2r p?orml2/p?unml2 p?ormr2/p?unmr2 p?pbtrsv p?pttrsv p?potf2 p?rot p?rscl p?sygs2/p?hegs2 p?sytd2/p?hetd2 p?trord p?trsen p?trti2 ?lahqr2 ?lamsh ?lapst ?laqr6 ?lar1va ?laref ?larrb2 ?larrd2 ?larre2 ?larre2a ?larrf2 ?larrv2 ?lasorte ?lasrt2 ?stegr2 ?stegr2a ?stegr2b ?stein2 ?dbtf2 ?dbtrf ?dttrf ?dttrsv ?pttrsv ?steqr2 ?trmvt pilaenv pilaenvx pjlaenv Additional ScaLAPACK Routines
0 kommentar(er)
