文章基本信息

标题：Hermitian Positive Definite Solution of the Matrix Equation <svg xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg" style="vertical-align:-5.4223pt" id="M1" height="21.7154pt" version="1.1" viewBox="-0.0657574 -16.2931 223.975 21.7154" width="223.975pt"><g transform="matrix(.018,0,0,-0.018,0,0)"><path id="g113-89" d="M748 650H522L515 622L546 617C580 611 587 604 565 575C518 513 469 451 419 393C376 474 349 534 330 580C318 609 325 612 361 618L383 622L392 650H151L144 622C214 616 224 612 257 543L360 327C270 218 187 124 159 95C106 40 92 34 26 28L17 0H252L259 28L236 31C189 37 188 47 209 78C249 136 308 210 377 294L478 79C494 44 487 37 449 32L418 28L409 0H673L680 28C596 34 591 39 554 116L436 361C526 469 574 521 604 553C659 612 669 614 739 622L748 650Z"/></g><g transform="matrix(.018,0,0,-0.018,18.678,0)"><path id="g117-34" d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"/></g><g transform="matrix(.018,0,0,-0.018,34.171,0)"><path id="g113-82" d="M699 368C699 549 574 666 407 666C186 666 23 488 23 277C23 113 129 -3 288 -13L307 -26C431 -111 501 -139 533 -147C559 -154 613 -163 658 -164L666 -141C597 -111 507 -66 430 -11L416 -1C580 42 699 190 699 368ZM601 371C601 227 518 54 381 22L354 40L278 24C175 47 120 145 120 269C120 451 235 631 398 631C540 631 601 521 601 371Z"/></g><g transform="matrix(.018,0,0,-0.018,51.081,0)"><path id="g117-36" d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"/></g><g transform="matrix(.018,0,0,-0.018,65.575,.009)"><path id="g119-65" d="M697 -46L668 -39C637 -126 611 -142 545 -142H163L474 298L206 694H483C558 694 584 688 600 668C615 651 627 625 639 580L667 585L655 739H70V714L378 254L53 -203V-228H655L697 -46Z"/></g><g transform="matrix(.013,0,0,-0.013,79.039,-8.796)"><path id="g50-110" d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z"/></g><g transform="matrix(.013,0,0,-0.013,79.039,5.206)"><path id="g50-106" d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z"/></g><g transform="matrix(.013,0,0,-0.013,82.544,5.206)"><path id="g54-34" d="M556 331V384H55V331H556ZM556 140V193H55V140H556Z"/></g><g transform="matrix(.013,0,0,-0.013,90.193,5.206)"><path id="g50-50" d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"/></g><g transform="matrix(.018,0,0,-0.018,100.008,0)"><path id="g113-66" d="M686 28C612 35 607 44 591 112C563 234 541 360 519 489L489 666L457 658L147 121C100 40 89 36 24 28L17 0H240L250 28C168 34 159 41 190 101L262 237H482C495 180 503 137 510 91C517 47 514 35 441 28L433 0H677L686 28ZM475 280H285L429 541H431L475 280Z"/></g><g transform="matrix(.013,0,0,-0.013,114.101,4.308)"><use xlink:href="#g50-106"/></g><g transform="matrix(.018,0,0,-0.018,118.277,0)"><path id="g113-41" d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"/></g><g transform="matrix(.018,0,0,-0.018,124.464,0)"><path id="g113-67" d="M578 512C578 619 494 650 387 650H140L134 622C219 615 223 609 210 542L127 119C112 40 104 34 23 28L17 0H235C317 0 387 7 444 33C515 65 564 122 564 195C564 289 495 335 412 352V354C505 373 578 422 578 512ZM486 510C486 422 423 367 314 367H257L294 565C299 591 305 602 315 608C324 614 339 617 362 617C421 617 486 595 486 510ZM466 200C466 100 393 35 296 35C222 35 198 51 212 127L250 333H303C388 333 466 303 466 200Z"/></g><g transform="matrix(.018,0,0,-0.018,139.21,0)"><use xlink:href="#g117-36"/></g><g transform="matrix(.018,0,0,-0.018,153.705,0)"><use xlink:href="#g113-89"/></g><g transform="matrix(.013,0,0,-0.013,167.385,-7.899)"><path id="g54-33" d="M556 236V289H56V236H556Z"/></g><g transform="matrix(.013,0,0,-0.013,175.035,-7.899)"><use xlink:href="#g50-50"/></g><g transform="matrix(.018,0,0,-0.018,181.841,0)"><path id="g113-42" d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"/></g><g transform="matrix(.013,0,0,-0.013,188.051,-8.249)"><use xlink:href="#g54-33"/></g><g transform="matrix(.013,0,0,-0.013,195.699,-8.249)"><use xlink:href="#g50-50"/></g><g transform="matrix(.018,0,0,-0.018,202.505,0)"><use xlink:href="#g113-66"/></g><g transform="matrix(.013,0,0,-0.013,215.072,-7.899)"><path id="g50-43" d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z"/></g><g transform="matrix(.013,0,0,-0.013,216.597,5.206)"><use xlink:href="#g50-106"/></g></svg>
本地全文：下载
作者：Chun-Mei Li ; Jing-Jing Peng
期刊名称：International Journal of Computational Mathematics
印刷版ISSN：2356-797X
出版年度：2014
卷号：2014
DOI：10.1155/2014/727093
出版社：Hindawi Publishing Corporation
摘要：We consider the Hermitian positive definite solution of the nonlinear matrix equation . Some new sufficient conditions and necessary conditions for the existence of Hermitian positive definite solutions are derived. An iterative method is proposed to compute the Hermitian positive definite solution. In the end, an example is used to illustrate the correctness and application of our results.