Accurate and Efficient Evaluation of Chebyshev Tensor Product Surface

<div>The relative forward error by using <span class="nowrap"><svg height="8.45082pt" id="M289" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -8.20528 20.6514 8.45082" width="20.6514pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M281 -11C384 -11 484 67 484 172C484 191 475 201 457 203H438C422 201 413 192 411 176C411 108 354 54 288 54C176 50 112 197 113 306C112 412 174 560 287 557C320 557 348 544 371 517S407 460 411 426C413 410 422 401 438 399H457C473 401 482 410 484 426V595C482 611 473 620 457 622H449C438 620 430 615 425 606L409 575C372 606 329 622 281 622C130 627 38 449 40 306C38 161 130 -16 281 -11Z" id="g204-36"></path></g><g transform="matrix(.013,0,0,-0.013,6.851,0)"><path d="M134 28C137 11 146 2 162 0H363C379 1 390 12 391 28V37C390 54 379 62 363 65H299V546H425V480C427 463 436 454 453 452H470C487 454 496 463 498 480V583C496 600 487 609 470 611H54C37 609 28 600 26 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410 484 426V595C482 611 473 620 457 622H449C438 620 430 615 425 606L409 575C372 606 329 622 281 622C130 627 38 449 40 306C38 161 130 -16 281 -11Z" id="g204-36"></path></g><g transform="matrix(.013,0,0,-0.013,34.253,0)"><path d="M134 28C137 11 146 2 162 0H363C379 1 390 12 391 28V37C390 54 379 62 363 65H299V546H425V480C427 463 436 454 453 452H470C487 454 496 463 498 480V583C496 600 487 609 470 611H54C37 609 28 600 26 583V480C28 463 37 454 54 452H71C87 455 98 463 99 480V546H226V65H162C146 63 137 54 134 37V28Z" id="g204-53"></path></g><g transform="matrix(.013,0,0,-0.013,41.104,0)"><path d="M24 28C26 11 35 2 52 0H211C228 2 237 11 239 28V37C237 54 228 63 211 65H168V241H295C396 241 480 327 480 426C480 527 396 611 295 611H52C35 608 26 599 24 583V574C25 558 37 547 52 546H95V65H52C35 63 26 54 24 37V28ZM168 546H277C312 546 342 535 368 512S407 461 407 426C407 358 343 306 277 306H168V546Z" id="g204-49"></path></g></svg>,</span> and <svg height="8.45082pt" id="M291" 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id="g204-49"></path></g></svg> to evaluate ill-conditioned polynomials.</div>

Mathematical Problems in Engineering

fig3

Figure 3

Figure 3: Accurate and Efficient Evaluation of Chebyshev Tensor Product Surface 